00000cmm a22000004a 4500 UP-99796217611212283 Buklod 20230215085534.0 m go j cr |nu|||auu|a 110502s2011 xx o u a eng d 9783642184291 (eBook) 3642184294 (eBook) (iLib)UPD-00215704038 DML eng DMLUC QA 55 L36 2011eb Lang, Jan. Eigenvalues, embeddings and generalised trigonometric functions [electronic resource] Jan Lang, David Edmunds. Berlin Heidelberg New York Springer c2011. 1 online resource (xi, 220 p.) Lecture notes in mathematics 2016 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. IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Website. 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Trigonometrical functions. Electronic books. Edmunds, D. E. (David Eric). SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-3-642-18429-1 FO Monograph UPD DMLR Electronic Resource