Eigenvalues, Embeddings and Generalised Trigonometric Functions

• Main Authors: Lang, Jan (Author), Edmunds, David (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2016
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Approximation theory.; Functional analysis.; Differential equations.; Special functions.; Mathematics > Study and teaching.; Analysis.; Approximations and Expansions.; Functional Analysis.; Special Functions.; Ordinary Differential Equations.; Mathematics Education.

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 wit...

Table of Contents:

• 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.