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- catalog abstract "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.".
- catalog contributor b11342119.
- catalog contributor b11342120.
- catalog contributor b11342121.
- catalog created "1999.".
- catalog date "1999".
- catalog date "1999.".
- catalog dateCopyrighted "1999.".
- catalog description "Includes bibliographical references and indexes.".
- catalog description "Preface -- 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 inverse operators for regulated and a.e. continuous functions -- Bibliographies on p-variation and phi-variation -- Subject Index -- Author Index.".
- catalog description "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.".
- catalog extent "viii, 277 p. ;".
- catalog hasFormat "Differentiability of six operators on nonsmooth functions and p-variation.".
- catalog identifier "3540659757 (alk. paper)".
- catalog isFormatOf "Differentiability of six operators on nonsmooth functions and p-variation.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1703.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1703".
- catalog issued "1999".
- catalog issued "1999.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Differentiability of six operators on nonsmooth functions and p-variation.".
- catalog subject "510 s 515/.7242 21".
- catalog subject "Differential operators.".
- catalog subject "Functions of bounded variation.".
- catalog subject "Global analysis (Mathematics)".
- catalog subject "Integrals.".
- catalog subject "Mathematics.".
- catalog subject "Operator theory.".
- catalog subject "QA3 .L28 no. 1703 QA329.4".
- catalog tableOfContents "Preface -- 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 inverse operators for regulated and a.e. continuous functions -- Bibliographies on p-variation and phi-variation -- Subject Index -- Author Index.".
- catalog title "Differentiability of six operators on nonsmooth functions and p-variation / Richard M. Dudley, Rimas Norvaǐsa.".
- catalog type "text".