03551nam 22007455 450 991014630790332120250730103442.09783540488149354048814610.1007/BFb0100744(CKB)1000000000437309(SSID)ssj0000322575(PQKBManifestationID)12072435(PQKBTitleCode)TC0000322575(PQKBWorkID)10283691(PQKB)10633647(DE-He213)978-3-540-48814-9(MiAaPQ)EBC5585318(Au-PeEL)EBL5585318(OCoLC)1066191013(MiAaPQ)EBC6859942(Au-PeEL)EBL6859942(PPN)155203649(EXLCZ)99100000000043730920121227d1999 u| 0engurnn#008mamaatxtccrDifferentiability of Six Operators on Nonsmooth Functions and p-Variation /by R. M. Dudley, R. Norvaiša1st ed. 1999.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1999.1 online resource (X, 282 p.)Lecture Notes in Mathematics,1617-9692 ;1703Bibliographic Level Mode of Issuance: Monograph9783540659754 3540659757 A survey on differentiability of six operators in relation to probability and statistics -- Product integrals, young integrals and p-variation -- Differentiability of the composition and quantile operators for regulated and A. E. continuous functions -- Bibliographies on p-variation and ?-variation.The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.Lecture Notes in Mathematics,1617-9692 ;1703Operator theoryGlobal analysis (Mathematics)Manifolds (Mathematics)Functions of real variablesOperator TheoryGlobal Analysis and Analysis on ManifoldsReal FunctionsOperator theory.Global analysis (Mathematics)Manifolds (Mathematics)Functions of real variables.Operator Theory.Global Analysis and Analysis on Manifolds.Real Functions.515.724Dudley R. M(Richard M.),48562Norvaiša Rimas1956-MiAaPQMiAaPQMiAaPQBOOK9910146307903321Differentiability of six operators on nonsmooth functions and p-variation262450UNINA