1.

Record Nr.

UNISA996466504703316

Autore

Lang Jan

Titolo

Eigenvalues, Embeddings and Generalised Trigonometric Functions [[electronic resource] /] / by Jan Lang, David E. Edmunds

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2011

ISBN

3-642-18429-4

Edizione

[1st ed. 2011.]

Descrizione fisica

1 online resource (XI, 220 p. 10 illus.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2016

Disciplina

515

Soggetti

Mathematical analysis

Analysis (Mathematics)

Approximation theory

Functional analysis

Special functions

Differential equations

Mathematics—Study and teaching 

Analysis

Approximations and Expansions

Functional Analysis

Special Functions

Ordinary Differential Equations

Mathematics Education

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.