Eigenvalues, embeddings and generalised trigonometric functions

✍ Scribed by Jan Lang, David Edmunds (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 239
• Series: Lecture Notes in Mathematics 2016
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Basic Material....Pages 1-31
Trigonometric Generalisations....Pages 33-48
The Laplacian and Some Natural Variants....Pages 49-63
Hardy Operators....Pages 65-71
s -Numbers and Generalised Trigonometric Functions....Pages 73-104
Estimates of s -Numbers of Weighted Hardy Operators....Pages 105-128
More Refined Estimates....Pages 129-151
A Non-Linear Integral System....Pages 153-182
Hardy Operators on Variable Exponent Spaces....Pages 183-209
Back Matter....Pages 211-220

✦ Subjects

Analysis; Approximations and Expansions; Functional Analysis; Special Functions; Ordinary Differential Equations; Mathematics Education