TY - BOOK ID - 17241129 TI - Differentiability of six operators on nonsmooth functions and p-variation AU - Dudley, Richard M. AU - Norvaisa, Rimas AU - Qian, Jinghua PY - 1999 VL - 1703 SN - 00758434 SN - 3540659757 3540488146 9783540659754 PB - Berlin ; Heidelberg ; New York Springer Verlag DB - UniCat KW - Differential operators KW - Functions of bounded variation KW - Differentiaaloperatoren KW - Fonctions à variation bornée KW - Functies met begrensde variatie KW - Integralen KW - Integrals KW - Intégrales KW - Operateurs differentiels KW - Operator theory. KW - Global analysis (Mathematics). KW - Manifolds (Mathematics). KW - Functions of real variables. KW - Operator Theory. KW - Global Analysis and Analysis on Manifolds. KW - Real Functions. KW - Real variables KW - Functions of complex variables KW - Geometry, Differential KW - Topology KW - Analysis, Global (Mathematics) KW - Differential topology KW - Geometry, Algebraic KW - Functional analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:17241129 AB - 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. ER -