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Stabile Approximation partieller Ableitungen auf Lp mit Hilfe von Wavelets

Stabile Approximation partieller Ableitungen auf Lp mit Hilfe von Wavelets

          
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About the Book

Inhaltsangabe: Einleitung: Das Hauptergebnis dieser Arbeit ist die Erweiterung spezieller Ergebnisse von Dinh Nho Hào, Hans-Jürgen Reinhardt und Adrian Schneider auf allgemeinere Funktionenklassen. Mit Hilfe von Wavelets entwickelten sie unter anderem ein Verfahren zur stabilen Approximation schwacher Ableitungen auf dem Hilbertraum L2(R). Meine Aufgabe war, dieses Verfahren in Theorie und Praxis für Banachräume Lp(Rn) mit Indizes 1

unendlich und n kleiner/gleich 1 zu verallgemeinern. Die Bearbeitung dieser Aufgabe gliedert sich wie folgt: In Kapitel 4 wird mit Hilfe spezieller Wavelets ein Verfahren zur stabilen Approximation partieller Ableitungen auf Banachräumen Lp(Rn) mit Indizes 1

unendlich und n Element N hergeleitet. Weitere Schwerpunkte sind die Demonstration der numerische Umsetzung des vorgestellten Verfahrens in Kapitel 5, sowie eine Einführung in die Theorie der Multiresolutionsanalyse für Funktionenräume Lp(Rn) mit Indizes p ungleich 2 in Kapitel 3. Eine knappe Darstellung einiger wichtiger Grundlagen findet man in Kapitel 2, die Diskussion der erzielten Ergebnisse und ein Ausblick auf artverwandte Probleme in Kapitel 6. Der Anhang enthält Nebenrechnungen, sowie eine Auflistung der im Zusammenhang mit dieser Arbeit verwendeten Software. Die beiden Fälle p=1 und p=unendlich bleiben in den folgenden Betrachtungen ausgeklammert, da die in dieser Arbeit verwendeten Methoden, in den entsprechenden Räumen, aus verschiedenen Gründen, nicht ohne weiteres angewendet werden können. Im Raum L1 existiert keine unbedingte Basis, wohingegen es im Raum L unendlich nicht einmal eine Schauder-Basis geben kann, da er nicht separabel ist. Die vorliegenden Ergebnisse erlauben jedoch die näherungsweise Betrachtung der ausgeschlossenen Grenzfälle. Nicht immer sind die Endpunkte der Skala [1, unendlich] die interessanten Fälle: Treten Polstellen auf, so kann die Messung der Abweichungen von den exakten Daten der Ordnung der Singularitäten angepaßt werden. Man kann das


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Product Details
  • ISBN-13: 9783838610016
  • Publisher: Diplom.de
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 9 mm
  • Width: 148 mm
  • ISBN-10: 3838610016
  • Publisher Date: 13 Aug 1998
  • Height: 210 mm
  • No of Pages: 154
  • Series Title: German
  • Weight: 213 gr


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