Differentiability of Six Operators on Nonsmooth Functions and p-Variation

  • Authors
  • Richard M. Dudley
  • Rimas Norvaiša

Part of the Lecture Notes in Mathematics book series (LNM, volume 1703)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. R. M. Dudley, R. Norvaiša
    Pages 73-208
  3. R. M. Dudley, R. Norvaiša, Jinghua Qian
    Pages 241-272
  4. Back Matter
    Pages 273-282

About this book

Introduction

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.

Keywords

Composition Hadamard differentiability Riemann-Stieltjes integrals convolution product-integral quantiel operator real analysis

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0100744
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-65975-4
  • Online ISBN 978-3-540-48814-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book