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Interpolationsmethoden Zur Behandlung Von Approximationsprozessen Auf Banachräumen

Interpolationsmethoden Zur Behandlung Von Approximationsprozessen Auf Banachräumen

          
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About the Book

In der klassischen Theorie der besten Approximation von stetigen periodischen Funktionen durch trigonometrische Polynome spielen die "direkten Sätze" von D. Jackson und die "Umkehrsätze" von s. Bernstein eine fundamentale Rolle. Ein Hauptanliegen der vorliegenden Abhandlung ist es, sich von den trigonometrischen Polynomen bester Approxima- tion loszulösen und enteprechende Sätze über Folgen von beschränkten linearen Transformationen, wie z. B. Summations- prozessen von Fourierreihen, zu beweisen, die gewisse Be- dingungen erfüllen. Diese Bedingungen sollen sicherstellen, daß das Phänomen der Saturation, welches bei allen gän- gen Prozessen gegeben ist, auftritt. Die Behandlung selbst erfolgt im abstrakten Rahmen der Theorie der Banachräume. Damit gelangt der Verfasser zu einem zentralen Problem, das letztlich darin besteht, den fundamentalen Satz, von Banach-Steinhaus über Folgen von beschränkten linearen Operatoren, und zwar die Aussage über notwendige und hin- reichende Bedingungen für die Konvergenz dieser Folgen gegen den Identitätsoperator, so zu verschärfen, daß er eine Aussage über die Konvergenzgeschwindigkeit liefert. Dieses grundlegende Problem ist schon seit m hreren Jah- ren in der Diskussion und wird vom Verfasser dahingehend behandelt, daß er in Banachunterräumen arbeitet, die sich als Interpolationsräume charakterisieren lassen.


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Product Details
  • ISBN-13: 9783540042341
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 1968 ed.
  • Language: German
  • Returnable: Y
  • Spine Width: 5 mm
  • Width: 156 mm
  • ISBN-10: 3540042342
  • Publisher Date: 01 Jan 1968
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 90
  • Series Title: Lecture Notes in Mathematics
  • Weight: 149 gr


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