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Lang, Jan.
Eigenvalues, Embeddings and Generalised Trigonometric Functions [electronic resource] / by Jan Lang, David Edmunds. - XI, 220p. 10 illus. online resource. - Lecture Notes in Mathematics, 2016 0075-8434 ; .
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.
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.
9783642184291
Mathematics.
Global analysis (Mathematics).
Functional analysis.
Differential Equations.
Functions, special.
Mathematics.
Analysis.
Approximations and Expansions.
Functional Analysis.
Special Functions.
Ordinary Differential Equations.
Mathematics Education.
QA299.6-433
515
Eigenvalues, Embeddings and Generalised Trigonometric Functions [electronic resource] / by Jan Lang, David Edmunds. - XI, 220p. 10 illus. online resource. - Lecture Notes in Mathematics, 2016 0075-8434 ; .
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.
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.
9783642184291
Mathematics.
Global analysis (Mathematics).
Functional analysis.
Differential Equations.
Functions, special.
Mathematics.
Analysis.
Approximations and Expansions.
Functional Analysis.
Special Functions.
Ordinary Differential Equations.
Mathematics Education.
QA299.6-433
515