Eigenvalues, embeddings and generalised trigonometric functions

The main theme of the book is the study, from the standpoint of s-numbers, ofintegral 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 tothe classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important exampleof 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. Review of recent developments in approximation theory for Hardy-type operators and Sobolev embeddings (description of the exact values of s-numbers and widths) - A special chapter devoted to the theory of generalized trigonometricfunctions (presented f INDICE: 1 Basic material. 2 Trigonometric generalisations. 3 The Laplacianand 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

• ISBN: 978-3-642-18267-9
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Rústica
• Páginas: 224
• Fecha Publicación: 01/04/2011
• Nº Volúmenes: 1
• Idioma: Inglés