Eigenvalues, Embeddings and Generalised Trigonometric Functions

ISBN-13: 9783642182679 / Angielski / Miękka / 2011 / 220 str.

Lang

Opis

This volume explores integral operators of Hardy type and related Sobolev embeddings from an s-numbers perspective. The text uses proof methods that incorporate the geometry of Banach spaces and generalized trigonometric functions.

Recenzje

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)

Spis treści

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

Blurb

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.