04285nam 22007935 450 99646650470331620231020165146.03-642-18429-410.1007/978-3-642-18429-1(CKB)2670000000076213(SSID)ssj0000506043(PQKBManifestationID)11313332(PQKBTitleCode)TC0000506043(PQKBWorkID)10513962(PQKB)10781943(DE-He213)978-3-642-18429-1(MiAaPQ)EBC3066565(PPN)151591342(EXLCZ)99267000000007621320110317d2011 u| 0engurnn#008mamaatxtccrEigenvalues, Embeddings and Generalised Trigonometric Functions[electronic resource] /by Jan Lang, David E. Edmunds1st ed. 2011.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2011.1 online resource (XI, 220 p. 10 illus.)Lecture Notes in Mathematics,0075-8434 ;2016Bibliographic Level Mode of Issuance: Monograph3-642-18267-4 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434 ;2016Mathematical analysisAnalysis (Mathematics)Approximation theoryFunctional analysisSpecial functionsDifferential equationsMathematics—Study and teaching Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Special Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M1221XOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Mathematics Educationhttps://scigraph.springernature.com/ontologies/product-market-codes/O25000Mathematical 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.515Lang Janauthttp://id.loc.gov/vocabulary/relators/aut478954Edmunds D. E(David Eric)authttp://id.loc.gov/vocabulary/relators/autBOOK996466504703316Eigenvalues, Embeddings and Generalised Trigonometric Functions2831054UNISA