Differentiability of Six Operators on Nonsmooth Functions and p-Variation

R. M. Dudley

ISBN 10: 3540659757 / ISBN 13: 9783540659754

Published by Springer Vieweg, Springer, 1999

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540659754

Bibliographic Details

• Title: Differentiability of Six Operators on Nonsmooth Functions and p-Variation
• Publisher: Springer Vieweg, Springer
• Publication Date: 1999
• Language: English
• ISBN 10: 3540659757
• ISBN 13: 9783540659754
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 233W x 155H x 16D millimeters 233 millimeters width by 155 millimeters height by 16 millimeters depth
• Weight: 443 grams

About this title

Synopsis

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.