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				<div style="text-align:left;margin-bottom:20px;">  		</div><span itemprop="name" class="title">Grundkurs Funktionalanalysis<br></span><p>Autoren:<br><span itemprop="author" class="author"><b>Winfried Kaballo</b></span></p><p>Verlag:<br><b itemprop="publisher">Spektrum-Akademischer Vlg</b>&nbsp;&nbsp;<a onclick="SearchPublEnt(680)" href="#">Weitere Titel dieses Verlages anzeigen</a></p>		
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<span class="notbold">Auflage: </span>2011. 2011.<br><span class="notbold">Erschienen: </span>März 2011<br><span class="notbold">Seiten: </span>345<br><span class="notbold">Sprache: </span>Deutsch<br><span class="notbold">Preis: </span>9.99 €<br><span class="notbold">Illustration: </span>75 schwarz-weiße Abbildungen
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						<h1><a href="_9783827421494_inhalt.html">Inhaltsverzeichnis</a></h1>
						<p><table><tr><td></td><td>Einleitung.....................................................• • •</td><td>1</td></tr><tr><td></td><td>I Banachräume und lineare Operatoren</td><td>7</td></tr><tr><td>1</td><td>Banachräume</td><td>8</td></tr><tr><td>1.1</td><td>Normen und Metriken</td><td>8</td></tr><tr><td>1.2</td><td>Supremums-Normen</td><td>13</td></tr><tr><td>1.3</td><td>Lp-Normen und Quotientenräume</td><td>15</td></tr><tr><td>1.4</td><td>Aufgaben</td><td>23</td></tr><tr><td>2</td><td>Kompakte Mengen</td><td>26</td></tr><tr><td>2.1</td><td>Der Satz von Arzelä-Ascoli</td><td>27</td></tr><tr><td>2.2</td><td>Separable Räume und ein Approximationssatz</td><td>31</td></tr><tr><td>2.3</td><td>Holder- und Sobolev-Normen</td><td>35</td></tr><tr><td>2.4</td><td>Aufgaben</td><td>38</td></tr><tr><td>3</td><td>Lineare Operatoren</td><td>41</td></tr><tr><td>3.1</td><td>Operatornormen</td><td>41</td></tr><tr><td>3.2</td><td>Isomorphien und Fortsetzungen</td><td>45</td></tr><tr><td>3.3</td><td>Lineare Operatoren auf endlichdimensionalen Räumen</td><td>48</td></tr><tr><td>3.4</td><td>Lineare Integral- und Differentialoperatoren</td><td>52</td></tr><tr><td>3.5</td><td>Aufgaben</td><td>55</td></tr><tr><td>4</td><td>Kleine Störungen</td><td>59</td></tr><tr><td>4.1</td><td>Banachalgebren und Neumannsche Reihe</td><td>59</td></tr><tr><td>4.2</td><td>Lineare Integralgleichungen</td><td>62</td></tr><tr><td>4.3</td><td>Grundlagen der Spektraltheorie</td><td>64</td></tr><tr><td>4.4</td><td>Der Banachsche Fixpunktsatz</td><td>69</td></tr><tr><td>4.5</td><td>Nicht lineare Integralgleichungen</td><td>71</td></tr><tr><td>4.6</td><td>Der Satz von Picard-Lindelöf</td><td>73</td></tr><tr><td>4.7</td><td>Aufgaben</td><td>75</td></tr><tr><td></td><td>II Fourier-Reihen und Hilberträume</td><td>81</td></tr><tr><td>5</td><td>Fourier-Reihen und Approximationssätze</td><td>82</td></tr><tr><td>5.1</td><td>Der Satz von Fejer</td><td>85</td></tr><tr><td>5.2</td><td>Faltung und Dirac-Folgen</td><td>89</td></tr><tr><td>5.3</td><td>Der Weierstraßsche Approximationssatz</td><td>91</td></tr><tr><td>5.4</td><td>Schwache Ableitungen und Sobolev-Räume</td><td>93</td></tr><tr><td>5.5</td><td>Punktweise Konvergenz von Fourier-Reihen</td><td>99</td></tr><tr><td>5.6</td><td>Aufgaben</td><td>101</td></tr><tr><td>6</td><td>Hilberträume</td><td>105</td></tr><tr><td>6.1</td><td>Die Parsevalsche Gleichung</td><td>108</td></tr><tr><td>6.2</td><td>Sobolev-Hilberträume und Fourier-Koeffizienten</td><td>113</td></tr><tr><td>6.3</td><td>Aufgaben</td><td>120</td></tr><tr><td>7</td><td>Lineare Operatoren auf Hilbert räumen</td><td>123</td></tr><tr><td>7.1</td><td>Lineare Operatoren und Matrizen</td><td>123</td></tr><tr><td>7.2</td><td>Orthogonale Projektionen</td><td>125</td></tr><tr><td>7.3</td><td>Adjungierte Operatoren</td><td>130</td></tr><tr><td>7.4</td><td>Selbstadjungierte und unitäre Operatoren</td><td>135</td></tr><tr><td>7.5</td><td>Aufgaben</td><td>139</td></tr><tr><td></td><td>III Prinzipien der Funktionalanalysis</td><td>143</td></tr><tr><td>8</td><td>Konsequenzen der Vollständigkeit</td><td>144</td></tr><tr><td>8.1</td><td>Der Satz von Baire</td><td>144</td></tr><tr><td>8.2</td><td>Das Prinzip der gleichmäßigen Beschränktheit</td><td>148</td></tr><tr><td>8.3</td><td>Der Satz von der offenen Abbildung</td><td>150</td></tr><tr><td>8.4</td><td>Anwendungen auf Fourier-Reihen</td><td>155</td></tr><tr><td>8.5</td><td>Aufgaben</td><td>158</td></tr><tr><td>9</td><td>Stetige lineare Funktionale</td><td>161</td></tr><tr><td>9.1</td><td>Der Fortsetzungssatz von Hahn-Banach</td><td>161</td></tr><tr><td>9.2</td><td>Duale Operatoren und Annihilatoren</td><td>166</td></tr><tr><td>9.3</td><td>Kanonische Einbettung und reflexive Räume</td><td>167</td></tr><tr><td>9.4</td><td>Beispiele von Dualräumen</td><td>171</td></tr><tr><td>9.5</td><td>Stetige Projektionen</td><td>175</td></tr><tr><td>9.6</td><td>Aufgaben</td><td>179</td></tr><tr><td>10</td><td>Schwache Konvergenz</td><td>182</td></tr><tr><td>10.1</td><td>Variationsprobleme</td><td>182</td></tr><tr><td>10.2</td><td>Trennung konvexer Mengen</td><td>186</td></tr><tr><td>10.3</td><td>Uniform konvexe Räume</td><td>190</td></tr><tr><td>10.4</td><td>Schwach konvergente Folgen</td><td>194</td></tr><tr><td>10.5</td><td>Schwach konvergente Teilfolgen</td><td>198</td></tr><tr><td>10.6</td><td>Aufgaben</td><td>202</td></tr><tr><td></td><td>IV Spektraltheorie kompakter und selbstadjungierter Operatoren</td><td>207</td></tr><tr><td>11</td><td>Fredholmoperatoren und kompakte Störungen</td><td>207</td></tr><tr><td>11.1</td><td>Kompakte lineare Operatoren</td><td>208</td></tr><tr><td>11.2</td><td>Fredholmoperatoren</td><td>214</td></tr><tr><td>11.3</td><td>Stabilität des Index</td><td>219</td></tr><tr><td>11.4</td><td>Spektren kompakter Operatoren</td><td>223</td></tr><tr><td>11.5</td><td>Aufgaben</td><td>225</td></tr><tr><td>12</td><td>Spektralzerlegungen</td><td>229</td></tr><tr><td>12.1</td><td>Modelle kompakter Operatoren</td><td>229</td></tr><tr><td>12.2</td><td>Der Spektralsatz für kompakte normale Operatoren</td><td>232</td></tr><tr><td>12.3</td><td>Hilbert-Schmidt-Operatoren</td><td>237</td></tr><tr><td>12.4</td><td>Singuläre Zahlen und Schmidt-Darstellungen</td><td>241</td></tr><tr><td>12.5</td><td>Schatten-Klassen und Integraloperatoren</td><td>246</td></tr><tr><td></td><td><div></td><td></td></tr><tr><td>12.6</td><td>Aufgaben</td><td>251</td></tr><tr><td>13</td><td>Unbeschränkte Operatoren</td><td>256</td></tr><tr><td>13.1</td><td>Abgeschlossene Operatoren</td><td>257</td></tr><tr><td>13.2</td><td>Adjungierte Operatoren</td><td>264</td></tr><tr><td>13.3</td><td>Symmetrische und selbst adjungierte Operatoren</td><td>267</td></tr><tr><td>13.4</td><td>Reguläre Sturm-Liouville-Probleme</td><td>272</td></tr><tr><td>13.5</td><td>Evolutionsgleichungen</td><td>280</td></tr><tr><td>13.6</td><td>Selbst adjungierte Operatoren und Quantenmechanik</td><td>283</td></tr><tr><td>13.7</td><td>Aufgaben</td><td>287</td></tr><tr><td></td><td>A Anhang</td><td>291</td></tr><tr><td></td><td>A.l Lineare Algebra</td><td>291</td></tr><tr><td></td><td>A.2 Metrische Räume und Kompaktheit</td><td>296</td></tr><tr><td></td><td>A.3 Maße und Integrale</td><td>304</td></tr><tr><td></td><td>A.3.1 Fortsetzung elementarer Integrale</td><td>306</td></tr><tr><td></td><td>A.3.2 Konvergenzsätze</td><td>312</td></tr><tr><td></td><td>A.3.3 Messbare Mengen und Funktionen</td><td>314</td></tr><tr><td></td><td>A.3.4 Die Sätze von Fubini und Tonelli</td><td>319</td></tr><tr><td></td><td>A.3.5 Der Rieszsche Darstellungssatz</td><td>324</td></tr><tr><td></td><td>Literaturverzeichnis</td><td>329</td></tr><tr><td></td><td>Index</td><td>331</td></tr><tr><td></td><td></td><td></td></tr></table></p>
					</section>	<section >
						<h1><a href="_9783827421494_register.html">Register</a></h1>
						<p><div>
<br></div>
Parseval, Marc-Antoine (1755-1836), 111, 
112, 115, 116<br/>Pelczynski, Alexander (*1932), 46<br/>Pettis, Billy James (1913-1979), 191<br/>Picard, Emile (1856-1941), 63, 73, 103<br/>Planck, Max (1858-1947), 68, 284<br/>Poisson, Simeon Denis (1781-1840), 90, 102<br/>Polya, Georg (1887-1985), 150<br/>Pythagoras (570-497 v. Chr.), 109<br/>Radon, Johann (1887-1956), 174<br/>Reilich, Franz( 1880-1956), 125<br/>Riemann, Bernhard (1826-1866), 99, 100, 104<br/>Riesz, Friedrich (1880-1956), 57, 62, 125, 
129, 171, 175, 223, 224<br/>Saks, Stanislaw (1897-1942), 148, 205<br/>Schatten, Robert (1911-1977), 246<br/>Schauder, Juliusz Pawel (1899-1943), 152, 160, 210<br>
Schmidt, Erhard (1876-1959), 51, 54, 129, 237, 242<br>
Schrödinger, Erwin (1887-1961), 283<br/>Schur, Issai (1875-1941), 196<br/>Schwarz, Hermann Amandus (1843-1921), 105<br>
Sierpinski, Waclaw (1882-1969), 322<br/>Smulian, Vitold L'vovich (1914-1944), 199<br/>Sobczyk, Andrew (1915-1981), 162<br/>Sobolev, Sergei L'vovich (1908-1989), 37, 48, 
93, 96, 98, 103<br/>Steinhaus, Hugo (1887-1972), 149, 171<br/>Steklov, Wladimir (1864-1926), 150<br/>Stieltjes, Thomas Jan (1856-1894), 174<br/>Stone, Marshall Harvey (1903-1989), 67, 287<br/>Sturm, Jacques Ch.F. (1803-1855), 183, 272, 275<br>
Szankowski, Andrzej Tomasz (*1945), 214<br/>Szasz, Otto (1884-1952), 165<br/>Szegö, Gabor (1895-1985), 150<br/>Taylor, Angus Ellis (1911-1999), 67<br/>Toeplitz, Otto (1881-1940), 132, 153<br/>Tonelli, Leonida (1885-1946), 321<br/>Tromba, Anthoy J. (*1943), 46<br/>Tschebyscheff, Pafnutij L. (1821-1894), 140<br/>Tzafriri, Lior (1936-2008), 176<br/>Volt er ra, Vito (1860-1940), 62, 63, 72, 73, 225, 243<br>
von Neumann, John (1903-1957), 59, 138, 
237, 246, 286<br/>Weierstraß, Karl (1815-1897), 27, 91, 97, 165<br/>Weyl, Hermann (1885-1955), 236, 247<br/>Yood, Bertram (1917-2004), 218, 219<br/>Young, William Henry (1863-1942), 114<br/>Zorn, Max August (1906-1993), 113, 163, 293<br>
<div>
<br></div>
<span class="bmhighl">Sachverzeichnis</span><br/>Ä<br>
a posteriori-Abschätzung, 70<br/>a priori-Abschätzung, 70<br/>Abbildung 
antilineare, 107<br/>bilineare, 159<br/>gleichmäßig stetige, 297<br/>isometrische, 15<br/>lineare, 41<br/>offene, 150<br/>stetige, 296<br/>Abel-Summe, 102<br/>abgeschlossene Menge, 298<br/>abgeschlossener Operator, 257<br/>Ableitung 
schwache, 94, 260<br/>Abschätzung a posteriori, 70<br/>a priori, 70<br/>Sobolev-, 37, 98<br/>von Eigenwerten, 237, 279<br/>von Fourier-Koeffizienten, 118<br/>abschließbarer Operator, 257<br/>Abschluss 
einer Menge, 298<br/>eines Operators, 259<br/>Absolutbetrag 
eines kompakten Operators, 241<br/>absolute Konvergenz, 20, 110<br>
von Fourier-Reihen, 118<br/>absolute Stetigkeit, 98, 104<br/>absolut konvexe Hülle, 186<br/>absolut konvexe Menge, 160, 186<br/>absolutsummierbare Familie, 107<br/>absorbierende Menge, 186<br/>abzählbare Teilüberdeckung, 39<br/>Addition 
von Operatoren, 260<br/>adjungierte Matrix, 131<br/>adjungierter Integraloperator, 132, 249<br/>adjungierter Operator, 130, 180, 264<br/>algebraische Vielfachheit, 223, 247<br/>Alternative 
Fredholmsche, 217, 235<br/>Anfangswertproblem, 62, 262, 281<br/>Annihilator, 166<br/>antilineare Abbildung, 107<br/>Approximation 
durch Polynome, 91, 97, 165<br/>durch Testfunktionen, 93<br/>durch trigonometrische Polynome, 88<br/>Approximationseigenschaft, 213, 226, 246, 253<br>
Approximationssatz, 33, 165<br>
von Müntz-Szäsz, 165<br/>Weierstraßscher, 36<br/>Approximationszahlen, 246, 253<br/>approximative Eins, 89, 102<br/>äquivalente Norm, 11, 12<br/>Äquivalenzklasse, 19, 21, 294<br/>Äquivalenzrelation, 19, 21, 294<br/>arithmetisches Mittel, 86<br/>assoziierter normierter Raum, 19<br/>Asymptotik 
von Eigenwerten, 251, 277<br/>Auswahlprinzip von Helly, 198<br>
<span class="bmhighl">B</span><br>
Bairescher Kategoriensatz, 145<br/>Banach-Limes, 179<br/>Banach- M azur- Distanz, 47<br/>Banachalgebra, 59<br/>Banachraum, 9, 20<br/>flach konvexer, 203<br/>flach normierter, 203<br/>reflexiver, 168, 170, 199, 200, 211<br/>separ abler, 169<br/>strikt konvexer, 184<br/>strikt normierter, 184<br/>uniform konvexer, 185<br/>Banachscher Fixpunktsatz, 70<br/>Bandmatrix, 139, 225<br/>Basis, 292<br>
algebraische, 292<br/>orthonormale, 111<br/>Schauder-, 160, 226<br/>beschränkte Folge, 13<br/>beschränkte Funktion, 13<br/>beschränkte Menge, 13, 23<br>
schwach beschränkte, 167<br/>beschränkte Variation, 115<br/>beschränkte Linearform, 42<br/>beschränkter linearer Operator, 42<br/>Besseische Ungleichung, 109, 195, 250<br/>Bestapproximation, 22, 49, 57<br/>Betrag 
eines kompakten Operators, 241<br/>Bidualraum, 167<br/>Bildraum, 41<br/>bilineare Abbildung, 159<br/>Bipolarensatz, 190<br/>Borel-Maß, 326<br/>Borel-Menge, 325<br/>Buckel 
gleitender, 205<br>
<span class="bmhighl">c 
Calkin-Algebra, 210, 218</span><br>
<div>
<br></div>
Cauchy-Folge, 9, 15, 20, 27<br>
schwache, 197<br/>Cauchysches Konvergenzkriterium, 9<br/>Cesàro-Konvergenz, 86, 88, 89, 102, 179, 205<br/>charakteristische Funktion, 304<br/>charakteristisches Polynom, 66<br>
<span class="bmhighl">D</span><br>
Definitionsbereich eines linearen Operators, 257<br>
ô -Funktional, 44, 90<br/>diagonal-dominante Matrix, 66<br/>Diagonalfolge, 30, 301<br/>Diagonalmatrix, 125, 230, 234<br/>Diagonaloperator, 77, 213, 231, 234, 258, 
262, 264<br/>Diagramm 
kommutatives, 170<br/>Differentialgleichung, 62, 73<br>
lineare, 62, 103<br/>Differentialoperator, 258, 262<br>
linearer, 55<br/>Differentiation fast überall, 98<br/>schwache, 94<br/>differenzierbarer Kern, 249, 250<br/>Diffusionsgleichung, 283<br/>Dimension, 146, 293<br/>Dirac-Folge, 89, 102<br/>Dirac-Funktional, 44, 90<br/>direkte Summe, 126, 294<br/>orthogonale, 127<br/>topologisch direkte, 176<br/>Dirichlet-Kern, 85, 101, 155<br/>Dirichlet-Problem, 277<br/>Dirichlet-Randbdingung, 272<br/>Dirichletsches Konvergenzkriterium, 89<br/>Dirichletsches Prinzip, 183<br/>diskrete Metrik, 296<br/>diskretes Spektrum, 263<br/>Distanz, 22, 25, 297<br>
Banach-Mazur-, 47<br/>Distanzfunktion, 297<br/>Drehung, 137<br/>Dreiecks-Ungleichung, 9<br/>dualer Operator, 166, 180<br/>Dualraum, 42<br/>von c, 172<br/>von c<sub>0</sub> , 56, 172<br/>von C(K), 175<br/>von £<sub>p</sub>, 171<br/>von L<sub>p</sub>(fi), 173, 194<br>
<span class="bmhighl">E</span><br>
Eichfunktional, 186<br>
Eigenfunktion 
eines Faltungsoperators, 125, 230<br/>eines Sturm-Liouville-Operators, 275<br/>Eigenvektor, 65, 284<br/>Eigenwerte, 65, 284<br>
Abschätzung, 237, 279<br>
algebraische Vielfachheit, 247<br>
Asymptotik, 251, 277<br>
eines Faltungsoperators, 125, 230<br>
eines Integraloperators, 251<br>
eines kompakten Operators, 224, 232, 233, 
236, 251<br/>eines Operators mit kompakten 
Resolventen, 263, 270<br/>eines Sturm-Liouville-Operators, 280<br/>geometrische Vielfachheit, 223<br/>Einbettung, 36<br/>kanonische, 167<br/>kompakte, 209<br/>Sobolev-, 120, 248, 277<br/>einfache Funktion, 304<br/>Einheitskugel, 10, 23<br/>Einheitssphäre, 46<br/>Eins 
approximative, 89, 102<br/>endlichdimensionaler Operator, 212, 237<br/>endlichdimensionaler Raum, 48<br/>Entwicklungssatz, 233, 270, 275, 286<br/>für Integraloperatoren, 240<br/>für Sturm-Liouville-Operatoren, 275<br/>c-Netz, 27<br/>e-Schlauch, 14<br/>Ergodensatz, 138, 205<br/>Er wart ungs wert, 283<br/>Erweiterung 
eines Operators, 257<br/>selbstadjungierte, 270<br/>Euklidische Norm, 11<br/>Eulersche Formel, 82, 112<br/>Eulersche Konstante, 155<br/>Evolutionsgleichung, 281, 284<br/>Existenz iterierter Integrale, 321<br>
<span class="bmhighl">F</span><br>
Faktorisierung 
eines Operators, 249, 250<br/>Faltung, 90, 102<br>
Faltungsoperator, 124, 131, 230, 251<br/>Familie, 107<br>
absolutsummierbare, 107<br/>quadratsummierbare, 108<br/>fast überall, 17, 309<br/>Fejer-Kern, 86-89, 91, 112<br/>Fixpunkt, 70<br>
flach konvexer Raum, 203<br/>flach normierter Raum, 203<br>
<div>
<br></div>
der Differential- und Integralrechnung, 97<br/>Heisenbergsche Unschärferelation, 290<br/>Heisenbergsche Vertauschungsrelation, 68, 290<br>
Hermite-Funktionen, 140<br/>Hermite-Polynome, 140<br/>Hilbert-Schmidt-Integraloperator, 240<br/>Hilbert-Schmidt-Norm, 51, 54, 124, 237<br/>Hilbert-Schmidt-Operator, 237, 244, 252<br/>Hilbertraum, 106, 214<br>
separabler, 113<br/>Hölder-Bedingung, 35, 100, 104, 116, 249, 
250<br>
Hölder-Norm, 35, 249, 250<br>
Hölder-Stetigkeit, 35, 249, 250<br>
Höldersche Ungleichung, 12, 17, 53, 106, 117<br>
Homöomorphie, 45, 64, 70<br>
Homotopie, 220<br>
Hülle 
absolut konvexe, 186<br/>konvexe, 10, 38<br/>lineare, 33, 292<br>
I<br>
Ideal, 61<br>
der kompakten Operatoren, 210<br/>Identitätssatz, 165<br/>Impulsoperator, 284, 290<br/>Index 
eines Fredholmoperators, 215, 219-222<br/>Inhalt, 309<br/>Inneres 
einer Menge, 298<br/>Input-Output-Analyse, 60<br/>Integral, 305<br/>Lebesgue-, 311<br/>Stieltjes-, 174<br>
vektorwertiger Funktionen, 180<br/>Integralgleichung, 62, 224<br/>Fredholmsche, 62, 76, 224<br/>Hammerstein-, 72<br/>Volterra-Hammerstein-, 73<br/>Volterrasche, 63, 243<br/>Integralnorm, 16, 308<br/>Integraloperator, 52, 62, 76, 208, 238, 249, 
251<br>
adjungierter, 132<br/>Hilbert-Schmidt-, 240<br/>kompakter, 209<br>
schwach singulärer, 58, 210, 225, 226<br/>singulare Zahlen, 250<br/>Volterrascher, 215, 225, 243<br/>Integraloperatoren Komposition, 58<br/>integrierbare Funktion, 305<br/>integrierbare Menge, 314<br>
Interpolation, 54, 113, 190<br/>invarianter Unterraum, 142<br/>Inverse 
einseitige, 227<br/>relative, 140, 152<br/>verallgemeinerte, 140, 152<br/>inverser Operator, 260<br/>Invertierbarkeit 
linearer Operatoren, 60, 64, 152<br/>modulo kompakter Operatoren, 218<br/>Isometrie, 15, 45, 56, 170<br/>Isomorphie, 45, 56, 57<br/>Iteration 
Picard-, 74<br/>iterierte Integrale, 321<br>
<span class="bmhighl">J</span><br>
Jensen-Formel, 165<br/>Jensensche Ungleichung, 192<br/>Jordan-Zerlegung, 104<br>
<span class="bmhighl">K</span><br>
kanonische Einbettung, 167<br/>Kategorie 
Bairesche, 144<br/>Kern, 41, 63<br>
differenzierbarer, 249, 250<br/>Dirichlet-, 85<br/>Fejér-, 86-89, 91, 112<br/>messbarer, 54, 323<br/>mit Hölder-Bedingungen, 249, 250<br/>quadratintegrierbarer, 210, 238, 322<br/>stetiger, 52, 63, 208, 249<br/>Kodimension, 215<br/>koerzive Form, 135<br/>kommutatives Diagramm, 170<br/>Kommutator, 68, 290<br/>kompakte Einbettung, 209<br/>kompakte Resolvente, 263<br/>kompakter Operator, 209, 217<br>
Schmidt-Darstellung, 242<br/>kompakter Träger, 34<br/>Kompaktheit, 13, 14, 26, 198, 199, 301,302<br/>in Co , 39<br>
in C(K), 29, 31, 36<br/>in C(K,Y), 31<br/>in C<sup>1</sup> [a, b] , 40<br/>in £p , 39<br/>Komplement 
eines Unterraumes, 126, 294<br/>orthogonales, 127<br/>topologisch direktes, 176<br/>komplementierter Unterraum, 176, 177, 198<br/>Komposition<br>
<span class="bmhighl">von Integraloperatoren, 58</span><br>
<div>
<br></div>
Konditionszahl 
einer Matrix, 52<br/>Kontraktion, 70<br/>konvergente Reihe, 20<br/>konvergente Teilfolge, 26<br/>Konvergenz 
absolute, 20, 118<br>
Cauchysches Konvergenzkriterium, 9<br/>Cesaro-, 86, 102, 205<br/>gleichmäßige, 13, 296, 297<br/>im Mittel, 16<br>
im quadratischen Mittel, 19, 112<br/>koordinatenweise, 11, 13<br/>lineare, 70<br>
monotone, 302, 309, 313<br/>punktweise, 14, 28, 146<br/>schwach*-, 194, 198<br/>schwache, 194, 199, 211<br/>in C(K), 195<br/>in Z<sub>x</sub> , 196<br/>in Z<sub>p</sub> , 196<br/>von Folgen, 9, 11<br/>von Operatorfolgen, 44, 149<br/>konvexe Funktion, 200<br/>konvexe Hülle, 10, 38<br/>konvexe Menge, 10<br/>Konvexität, 18<br/>Konvexkombination, 10<br/>koordinatenweise Konvergenz, 11, 13<br/>kreisförmige Menge, 203<br/>Kronecker-Symbol, 83<br/>Kugel, 10<br>
<span class="bmhighl">L</span><br>
Laplace-Operator, 183, 284<br/>Laurent-Entwicklung, 168<br/>Lebesgue-Integral, 311<br/>Lebesgue-Zahl, 302<br/>Legendre-Polynome, 130, 140<br/>Leibniz-Kriterium, 89<br/>Leibniz-Reihe, 89<br/>Lemma 
Rieszsches, 57<br/>von Auerbach, 58, 177<br/>von Ehrling, 226, 273<br/>von Fatou, 313<br/>von Kato, 216, 227<br/>von Riemann-Lebesgue, 99, 195<br/>Zornsches, 113, 163, 164, 293<br/>Lifting 
stetiger linearer Operatoren, 181<br/>Limes superior, 61<br/>Limitierungen, 86, 102<br/>lineare Differentialgleichung, 62, 103, 183<br/>lineare Gleichung, 216<br/>lineare Hülle, 33, 292<br>
lineare Konvergenz, 70<br/>lineare Unabhängigkeit, 292<br/>linearer Differentialoperator, 55<br/>linearer Operator, 257<br>
i—» Operator lineares Gleichungssystem, 52<br>
unendliches, 76<br/>Linearform, 292<br/>auf c, 172<br/>auf co , 172<br/>auf C(K), 175<br/>auf Zp , 171<br/>auf LpO), 173, 194<br/>auf einem Hilbertraum, 129<br/>beschränkte, 42<br/>Fortsetzung, 162, 164<br/>stetige, 42<br/>Linksinverse, 77, 227<br/>Lipschitz-Bedingung, 35, 71, 73<br/>Lipschitz-Stetigkeit, 69, 98<br/>lokale Reflexivität, 191<br/>Lokalisierungssatz 
Riemannscher, 100, 104<br/>Lösbarkeit von Gleichungen, 133, 167, 266<br/>Ci -Majorante, 314<br>
<span class="bmhighl">M</span><br>
magere Menge, 144, 159<br/>Majorante, 308<br/>Maß, 16, 309, 314<br/>positives, 16<br/>Zählmaß, 16<br/>Maßraum 
vollständiger, 315<br/>Matrix, 50<br>
-Darstellung, 123<br/>diagonal-dominante, 66<br/>Diagonalmatrix, 125, 230<br/>Konditionszahl, 52<br/>-Normen, 50-51<br/>Matrizenmechanik, 124<br/>maximales Orthonormalsystem, 108<br/>MaxiMin-Prinzip, 251<br/>Maximum 
einer stetigen Linearform, 168<br/>Menge 
abgeschlossene, 298<br/>absolut konvexe, 160, 186<br/>absorbierende, 186<br/>beschränkte, 13, 23<br/>Gs -, 148<br/>integrierbare, 314<br/>kompakte, 13, 14<br/>konvexe, 10<br/>kreisförmige, 203<br/>magere, 144, 159<br>
<div>
<br></div>
messbare, 304<br/>nirgends dichte, 144<br/>offene, 298<br/>präkompakte, 27, 38<br/>relativ kompakte, 27<br/>schwach beschränkte, 167<br/>schwach folgenkompakte, 199<br/>schwach *-folgenkompakte, 198<br/>messbare Menge, 304<br/>messbare Funktion, 304<br/>messbarer Kern, 54, 323<br/>Messergebnisse, 283<br/>Methode 
des gleitenden Buckels, 205<br/>Metrik, 9, 24<br>
diskrete, 296<br/>metrische Projektion, 126<br/>metrischer Raum, 9<br/>Minimalfolge, 126, 200<br/>MiniMax-Prinzip, 236, 241, 279<br/>Minimum, 13<br>
eines Funktionais, 183, 200, 201<br/>Minkowski-Funktional, 186<br/>Minkowskische Ungleichung, 18<br/>Mittel 
arithmetisches, 86<br/>Mittelwertsatz der Differentialrechnung, 28, 29<br>
Momentenproblem, 180<br/>Multiplikationsoperator, 77, 131, 225, 258, 
262, 264, 287<br/>H -Majorante, 308<br/>//-Obersumme, 308<br/>/i-fast überall, 309<br>
<span class="bmhighl">N</span><br>
Nemytskij-Operator, 71<br/>Neumann-Randbedingung, 277<br/>Neumannsche Reihe, 60, 75, 121<br/>nilpotenter Operator, 68<br/>nirgends dichte Menge, 144<br/>Norm, 9, 106<br>
äquivalente, 11, 12<br/>C'<sup>m</sup>-, 37<br>
einer stetigen Linearform, 168<br/>Euklidische, 11<br/>Graphennorm, 257<br/>Hilbert-Schmidt-, 51, 54, 124<br/>Holder-, 35, 249, 250<br>
V, <sup>11</sup><br>
Lp-, 16, 19<br/>Operator-, 42<br/>Quotienten-, 21, 25<br/>Sobolev-, 37, 114<br/>Sobolev-Slobodeckij-, 116, 250<br/>Spaltenintegral-, 52, 323<br>
Spaltensummen-, 51, 124<br/>sup-, 13<br>
Zeilenintegral-, 52, 323<br/>Zeilensummen-, 51, 124<br/>normal auflösbare Gleichung, 134, 152<br/>normaler Fredholmoperator, 216, 235<br/>normaler Operator, 130, 137, 233<br/>normierter Raum, 9<br/>nuklearer Operator, 254<br/>Nullfunktion, 18, 309<br/>Nullmenge, 17, 104, 159, 309<br/>Nullraum, 41<br>
numerischer Wertebereich, 141<br>
o 
oberhalbstetige Funktion, 200, 302<br/>Obersumme, 308<br/>Observable, 283<br/>offene Abbildung, 21, 150<br/>offene Menge, 298<br>
im R<sup>n</sup> , 299<br/>offene Uberdeckung, 26<br/>Operator 
abgeschlossener, 257<br/>abschließbarer, 257<br/>Abschluss, 259<br/>adjungierter, 130, 180, 264<br/>Diagonal-, 77, 213<br/>dualer, 166, 180<br/>endlichdimensionaler, 212, 237<br/>Erweiterung, 257<br/>Faltungs-, 124, 131, 230, 251<br/>Fortsetzung, 175, 178<br/>Fredholmoperator, 215, 218<br/>Graph, 257<br/>Hammerstein-, 71<br/>Hammerstein-Volterra-, 71<br/>Hilbert-Schmidt-, 237, 244<br/>Integral-, 62<br/>inverser, 260<br/>invertierbarer, 64<br/>kompakter, 209, 217<br/>Lifting, 181<br/>linearer, 41, 257<br/>linksinvertierbarer, 77<br/>mit diskretem Spektrum, 263<br/>mit kompakten Resolventen, 263<br/>Multiplikations-, 77, 225<br/>Nemytskij-, 71<br/>nilpotenter, 68<br/>normaler, 130, 137<br/>nuklearer, 254<br/>positiv definiter, 236<br/>positiver, 236<br/>quasinilpotenter, 68<br/>rechtsinvertierbarer, 77<br>
<div>
<br></div>
der Lebesgue-integrierbaren Funktionen, 34<br>
der Nullfolgen, 13, 24, 169, 172, 176, 179<br/>der Nullfunktionen, 18, 309, der p -summierbaren Folgen, 171, 172<br/>der p -summierbaren Funktionen, 16, 19, 
173, 184, 193, 194<br/>der stetig differenzierbaren Funktionen, 36<br/>der stetigen Funktionen, 14, 31, 170<br/>der summierbaren Folgen, 172, 181, 196, 197<br>
der Testfunktionen, 93<br>
der wesentlich beschränkten Funktionen, 
17, 178<br/>endlichdimensionaler, 48<br/>flach konvexer, 203<br/>flach normierter, 203<br/>Folgenraum, 13, 16, 24<br/>Hölder-stetiger Funktionen, 35, 178<br/>kompakter, 26, 302<br/>metrischer, 9<br/>normierter, 9<br>
periodischer Funktionen, 114<br/>präkompakter, 27<br/>Quotientenraum, 19, 21, 171, 294<br/>reflexiver, 168, 170, 191, 199, 200, 211<br/>relativ kompakter, 27<br/>separabler, 30, 31, 34, 39, 164, 179<br/>Sobolev-, 37, 96, 98, 103, 183, 201, 269<br/>strikt konvexer, 184<br/>strikt normierter, 184<br/>total beschränkter, 27<br/>uniform konvexer, 185, 193<br/>Vervollständigung, 15<br/>vollständiger, 9, 70<br/>vollständiger normierter, 9, 24<br/>Rechtsinverse, 77, 177, 198, 227<br/>rechtsinvertier bare Quotientenabbildung, 177, 198<br>
reflexiver Banachraum, 168, 170, 191, 199, 200, 211<br/>Reflexivität 
lokale, 191<br/>Regularitätssatz, 103, 184, 274<br/>Reihe 
absolut konvergente, 20, 110<br/>Fourier-Reihe, 82, 84<br/>geometrische, 60<br/>konvergente, 20<br/>Neumannsche, 60<br/>unbedingt konvergente, 110<br/>relativ kompakte Menge, 27<br/>relative Inverse, 140, 152<br/>Resolvente, 64, 78, 261<br>
eines selbstadjungierten Operators, 135, 269<br>
Holomorphie, 65<br>
kompakte, 263<br/>Resolventengleichung, 64, 288<br/>Resolventenmenge, 64, 261<br/>Retraktion, 126<br>
Riemann-Lebesgue Lemma, 99, 195<br/>Riemannscher Lokalisierungssatz, 100, 104<br/>Rieszscher Darstellungssatz, 107, 129, 173, 
175, 264<br/>Rieszsches Lemma, 57<br/>Ring 
von Mengen, 306<br>
<span class="bmhighl">s 
Satz 
Approximationssatz, 33</span><br/>Banachscher Fixpunktsatz, 70<br/>Bipolarensatz, 190<br/>des Pythagoras, 109<br/>Fortsetzungssatz, 47, 178<br/>Fundamentalsatz der Algebra, 66<br/>Lemma von Fatou, 313<br/>Liftingsatz, 181<br>
MiniMax-Prinzip, 236, 241, 279<br/>Prinzip der gleichmäßigen Beschränktheit, 
148, 195, 205<br/>Regularitätssatz, 103, 184, 274<br/>Riemann-Lebesgue Lemma, 99, 195<br/>Riemannscher Lokalisierungssatz, 100, 104<br/>Rieszscher Darstellungssatz, 107, 129, 
173, 175, 264<br/>Sobolevscher Einbettungssatz, 98<br/>Spektralsatz 
für kompakte normale Operatoren, 233<br/>für selbstadjungierte Operatoren, 286<br/>für selbst adjungierte Operatoren mit kompakten Resolventen, 270<br/>Trennungssatz, 187, 189<br/>über majorisierte Konvergenz, 94, 314<br/>über monotone Konvergenz, 313<br/>vom abgeschlossenen Bild, 267<br/>vom abgeschlossenen Graphen, 153<br/>vom inversen Operator, 152<br/>von Alaoglu-Bourbaki, 199<br/>von Arzelä-Ascoli, 31, 53, 208<br/>von Baire, 145<br/>von Banach-Hausdorff, 267<br/>von Banach-Mazur, 78<br/>von Banach-Saks, 205<br/>von Banach-Steinhaus, 149<br/>von B. Levi, 19, 312<br>
L<sub>p</sub> - Version, 318<br/>von Bolzano-Weierstraß, 27<br/>von Carleson-Hunt, 158<br/>von Cavalieri, 322<br>
von der offenen Abbildung, 152, 216<br/>von Dini, 99, 302, 311<br>
<div>
<br></div>
von Dirichlet-Jordan, 101<br/>von Eberlein-Smulian, 199<br/>von Fejer, 88, 89, 91, 112<br/>von Fubini, 320<br>
von Hahn-Banach, 67, 162, 164, 195<br>
von Hausdorff-Young, 114<br>
von Hellinger-Toeplitz, 153<br>
von Helly, 190<br>
von Lax-Milgram, 139<br>
von Lebesgue, 314<br>
von Lidskii, 255<br>
von Liouville, 66, 68<br>
von Müntz-Szäsz, 165<br>
von Mazur, 200<br>
von Milman-Pettis, 191<br>
von Milutin, 46<br>
von Osgood, 144<br>
von Picard-Lindelöf, 63, 73, 103<br>
von Polya-Szegö, 150<br>
von Riesz, 129, 173, 175, 224, 264<br>
von Schauder, 210, 214<br>
von Schur, 196, 211<br>
von Sobczyk, 179, 181<br>
von Steklov, 150<br>
von Stone, 287<br>
von Tonelli, 54, 321<br>
Weierstraßscher Approximationssatz, 36, 
91, 97, 165<br/>Zornsches Lemma, 113, 163, 164, 293<br/>Schatten-Klassen, 246<br/>Schauder-Basis, 160, 226<br/>Schmidt-Darstellung, 230, 242<br/>Schnittmenge, 322<br/>Schrödinger-Gleichung, 284<br/>schwach beschränkte Menge, 167<br/>schwach konvergente Folge, 194, 211<br/>in C(K), 195<br/>in h , 196<br/>in £<sub>p</sub> , 196<br/>schwach konvergente Teilfolge, 199<br/>schwach*-konvergente Folge, 194<br>
in t'<sub>v</sub> , 196<br/>schwach*-konvergente Teilfolge, 198<br/>schwach singulärer Integraloperator, 58, 210, 
225, 226<br/>schwache Ableitung, 94, 260<br/>Schwarzsche Ungleichung, 105<br/>Schwingungen, 82<br/>selbstadjungierte Erweiterung, 270<br/>selbstadjungierter Operator, 130, 135, 136, 268<br>
Semi-Fredholmoperator, 227<br/>separabler Banachraum, 197<br/>separabler Dualraum, 169<br/>separabler Hilbertraum, 113<br>
separabler Raum, 30, 31, 34, 39, 98, 164, 
169, 179<br/>Sesquilinearform, 139<br/>Shift-Operator, 66, 77, 132, 141, 215, 221<br/>er-Algebra, 304, 314<br/>er-endliches Maß, 317<br/>Signum-Funktion, 95<br/>singulare Zahlen, 241, 242, 244, 245<br>
von Integraloperatoren, 250<br/>Skalarprodukt, 105<br/>Sobolev-Abschätzung, 37, 98<br/>Sobolev-Einbettung, 48, 98, 120, 133, 244, 
248, 274, 277<br/>Sobolev-Norm, 37, 114<br>
Sobolev-Raum, 37, 96, 98, 103, 114, 122, 183,.<br>
201, 269, 272<br/>Sobolev-Slobodeckij-Norm, 116, 250<br/>Spaltenintegral-Norm, 52, 323<br/>Spaltensummen-Norm, 51, 61, 124<br/>Spektralintegral, 286<br/>Spektralmaß, 286<br/>Spektralradius, 61, 65, 73, 168<br>
normaler Operatoren, 137<br/>Spektralsatz 
für kompakte normale Operatoren, 233<br/>für kompakte selbst adjungierte 
Operatoren, 234<br/>für selbstadjungierte Operatoren, 286<br/>für selbstadjungierte Operatoren mit kompakten Resolventen, 270<br/>Spektrum, 64, 107, 161, 168, 261, 263, 283<br/>eines selbstadjungierten Operators, 135, 269<br>
eines Shift-Operators, 221<br/>kompakter Operatoren, 224<br/>nicht leeres, 67, 164<br/>Spur 
eines Operators, 254<br/>Spurformel, 255<br/>Spurklasse, 247<br/>Stabilität 
des Index, 220-222<br/>von Orthonormalbasen, 121<br/>stetig projizierter Unterraum, 176, 177, 198<br/>stetige Einbettung, 120<br/>stetige Funktion, 14<br/>stetige Linearform, 42, 168<br>
Fortsetzung, 164<br/>stetige Projektion, 176<br/>stetige Zerlegung der Eins, 32<br/>stetiger Kern, 52, 208, 249<br/>stetiger linearer Operator, 41<br/>Stetigkeit, 296<br/>absolute, 98, 104<br/>gleichgradige, 28, 43<br/>gleichmäßige, 28<br/>Holder-, 35<br>
<div>
<br></div>
inverser Operatoren, 152<br/>linearer Abbildungen, 41<br/>Lipschitz-, 98<br>
von Grenzfunktionen, 28, 146, 297<br/>Stieltjes-Integral, 174<br/>Störung 
lineare, 60<br/>nicht lineare, 70<br/>kleine, 220<br/>kompakte, 220<br/>Streuung, 290<br/>strikt konvexer Raum, 184<br/>strikt normierter Raum, 184<br/>stückweise C<sup>1</sup> -Funktion, 104<br/>Sturm-Liouville-Problem, 183, 272, 275, 280, 289<br>
sublineares Funktional, 162, 187<br/>Summe 
direkte, 127<br/>einer Familie, 108<br/>orthogonale, 127<br/>topologisch direkte, 176<br/>von Operatoren, 260<br/>sup-Norm, 13<br>
symmetrischer Operator, 268<br/>System 
von Differentialgleichungen, 62, 103<br>
<span class="bmhighl">T</span><br>
Teilüberdeckung abzählbare, 39<br/>Teilfolge 
Cauchy-, 27<br/>konvergente, 20, 26<br/>Tensorprodukt, 33<br/>Testfunktion, 183, 260<br/>Thermodynamik, 138<br/>Toeplitz-Matrix, 132<br/>Tonne, 160<br>
topologisch direkte Summe, 176<br/>total beschränkter Raum, 27<br/>totale Variation, 104<br/>Träger 
einer Familie, 107<br/>einer Funktion, 32, 307<br/>kompakter, 34<br/>Translationsoperator, 57<br/>transponierter Operator, 166<br/>Transposition, 50<br/>Trennungssatz, 164, 187, 189<br/>Treppenfunktion, 307<br/>trigonometrisches Polynom, 91<br/>Tschebyscheff-Polynome, 140<br>
<span class="bmhighl">U</span><br>
Uberdeckung 
abzählbare Teilüberdeckung, 39<br/>offene, 26<br/>unbedingte Konvergenz, 110<br/>unendliches lineares Gleichungssystem, 76<br/>Ungleichung 
Besseische, 109, 195<br/>Dreiecks-, 9<br/>Höldersche, 12, 17, 106<br/>Jensensche, 192<br/>Minkowskische, 18<br/>Schwarzsche, 105<br/>Weyische, 247, 251<br/>uniform konvexer Raum, 185, 193<br/>unitäre Äquivalenz, 252<br/>unitärer Operator, 130, 137, 285<br/>Unschärferelation 
Heisenbergsche, 290<br/>unstetiger linearer Operator, 55<br/>unterhalbstetige Funktion, 200<br/>Unterraum, 291<br/>invarianter, 142<br>
komplementierter, 176, 177, 198<br/>reflexiver, 171<br>
stetig projizierter, 176, 177, 198<br>
<span class="bmhighl">V</span><br>
Variation 
eines Funktionais, 183, 200-202<br/>beschränkte, 98, 101, 104, 115<br/>totale, 104<br/>Vektorraum, 291<br>
verallgemeinerte Inverse, 140, 152<br/>Vertauschungsrelation Heisenbergsche, 290<br/>Vervollständigung, 15, 167<br/>Vielfachheit 
algebraische, 223, 247<br/>geometrische, 223<br/>vollständiger Maßraum, 315<br/>vollständiges Orthonormalsystem, 111<br/>Vollständigkeit, 145<br/>metrischer Räume, 9<br/>normierter Räume, 20<br/>von Dualräumen, 43<br/>von loo -Räumen, 14<br/>von £<sub>p</sub> -Räumen, 24<br/>von L<sub>p</sub> -Räumen, 19, 318<br/>von Quotientenräumen, 22<br/>von Räumen linearer Operatoren, 43<br/>von Sobolev-Räumen, 96<br/>vollstetiger Operator, 211<br/>Volterra-Hammerstein-Integralgleichung, 73<br/>Volterra-Operator, 66, 215, 225, 243<br/>Volterrasche Integralgleichung, 63<br>

<span class="bmhighl">W</span><br>
Wärmeleitungsgleichung, 281, 283<br/>Weierstraßscher Approximationssatz, 36, 91, 
97, 165<br/>Wellenmechanik, 124<br/>wesentlich beschränkte Funktion, 17<br/>wesentliches Supremum, 17, 54<br/>Wey Ische Ungleichung, 247, 251<br/>Würfel, 299<br/>Wurzel 
eines kompakten positiven Operators, 241<br>
<span class="bmhighl">z 
Zählmaß, 16</span><br/>Zahlen 
Approximations-, 253<br/>Gelfand, 253<br>
singuläre, 241, 242, 244, 245<br/>Zeilenintegral-Norm, 52, 323<br/>Zeilensummen-Norm, 51, 124<br/>Zerlegung der Eins, 77<br>
stetige, 32<br/>Zerlegungseigenschaft, 306<br/>Zornsches Lemma, 113, 163, 164, 293<br/>Zustand, 283<br/>zweiseitiges Ideal, 61<br><div>
<br></div>
</p>
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