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© 1999

Differentiability of Six Operators on Nonsmooth Functions and p-Variation

  • Authors
Book

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

  • Book Title Differentiability of Six Operators on Nonsmooth Functions and p-Variation
  • Authors R. M. Dudley
    R. Norvaiša
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI https://doi.org/10.1007/BFb0100744
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-65975-4
  • eBook ISBN 978-3-540-48814-9
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages X, 282
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
    Global Analysis and Analysis on Manifolds
    Real Functions
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