Eigenvalues, Embeddings and Generalised Trigonometric Functions - Lang, Jan.; Edmunds, David; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2011)
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.
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.
Keywords: Mathematics; Global analysis (Mathematics).; Functional analysis; Differential Equations; Functions, special; Mathematics; Analysis; Approximations and Expansions; Functional Analysis; Special Functions; Ordinary Differential Equations; Mathematics Education