Hilbertsche Räume Mit Kernfunktion

Name: Hilbertsche Räume Mit Kernfunktion
Brand: Springer
SKU: 9783642948497
Price: 3776.0 INR
Availability: InStock

by Herbert Meschkowski

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ISBN13: 9783642948497
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: February 22, 2012
Pages: 260
Original Price: EUR 51.39
Language: German
Edition: Softcover Repri
Item Weight: 381 grams
BISAC Subject(s): General

About The Book

Die Hilbertschen Raume mit reproduzierendem Kern gehoren zu jenen mathematischen Strukturen, die sich in vielen Gebieten der Analysis anwenden lassen. Manche Klassen von analytischen Funktionen (von einer oder mehreren komplexen Veranderlichen), aber auch gewisse Mengen von L6sungen partieller Differentialgleichungen erweisen sich als Hilbertsche Funktionenraume, die einen reproduzierenden Kern besitzen. Bald nach Erscheinen der grundlegenden Arbeiten von BERGMAN und BOCHNER im Jahre 1922 (s. Literaturverzeichnis) wurde klar, daB die Einffihrung von "Kernfunktionen" besonders fUr die Theorie der konformen Abbildung fruchtbar werden muBte. Wahrend in der von KOEBE und seinen Schiilern begrfindeten Theorie viele Satze den Cha- rakter reiner Existenzaussagen hatten, gelang es mit Hilfe der Kern- funktionen, die klassischen Abbildungsfunktionen explizit darzustellen und damit ihre effektive Berechnung zu erleichtern. In frfiheren Darstellungen fiber die Kernfunktionen hat man meist die Bedeutung der neuen Betrachtungsweise ffir die einzelnen Disziplinen getrennt herausgestellt. Bei einer so1chen fibergreifenden TheOl"ie ist es aber auch moglich, von den allgemeinen Eigenschaften Hilbertscher Funktionenraume mit Kernfunktion auszugehen. Besonders die um- fassende Arbeit von ARONSZAJN [1] hat eine so1che Darstellungsweise nahe gelegt. Sie macht es moglich, Wiederholungen zu vermeiden und allgemeine Eigenschaften der Kernfunktionen als so1che herauszustellen. Urn diese Schrift auch fUr Student en der mittleren Semester lesbar zu machen, beginnen wir mit einem Kapitel fiber die allgemeinen Hilbertschen Raume. Wir beschranken uns dabei auf den Beweis so1cher Satze, die ffir die hier behandelte Theorie gebraucht werden.

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