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Lang, Jan; Edmunds, David

Eigenvalues, Embeddings and Generalised Trigonometric Functions (Kartoniert / Broschiert / Paperback)

Reihe: Lecture Notes in Mathematics 2016

Springer-Verlag GmbH, März 2011

220 S. - Sprache: Englisch - 10 schwarz-weiße Abbildungen - 238x157x18 mm Book

ISBN: 3642182674 EAN: 9783642182679

The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.

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- Review of recent developments in approximation theory for Hardy-type operators and Sobolev embeddings (description of the exact values of s-numbers and widths) - A special chapter devoted to the theory of generalized trigonometric functions (presented for the first time in a book) - Description of connections between optimal approximations, eigenvalues for the p-Laplacian and generalized trigonometric functions


1 Basic material.- 2 Trigonometric generalisations.- 3 The Laplacian and some natural variants.- 4 Hardy operators.- 5 s-Numbers and generalised trigonometric functions.- 6 Estimates of s-numbers of weighted Hardy operators.- 7 More refined estimates.- 8 A non-linear integral system.- 9 Hardy operators on variable exponent spaces


From the reviews:"This well-written book deals with asymptotic behavior of the s-numbers of Hardy operators on Lebesgue spaces via methods of geometry of Banach spaces and generalized trigonometric functions. ... This book contains many interesting results that are proved in detail and are usually preceded by technical lemmas. The list of references is very rich and up to date. Many open problems are pointed out. We warmly recommend it." (Sorina Barza, Mathematical Reviews, Issue 2012 e)

ISBN 3-642-18267-4

ISBN 978-3-642-18267-9

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