Differentiability of six operators on nonsmooth functions and p-variation
By: Richard M. Dudley, Rimas Norvaiša, with the collaboration of Jinghua Qian.
Contributors: Norvaiša, Rimas, 1956-; Qian, Jinghua.
Series: Lecture notes in mathematics,; 1703; Lecture notes in mathematics (Springer-Verlag) ;; 1703.
Publisher: Springer
Published: 1999
Place of publication: Berlin; New York
Language: eng
Number of pages: 277
Subjects: Differential operators; Functions of bounded variation; Integrals
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.
Notes: Includes bibliographical references and indexes.