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Differentiability of Six Operators on Nonsmooth Functions and p-Variation

  • Book
  • © 1999

Overview

Authors:
  1. Richard M. Dudley
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  2. Rimas NorvaiĊĦa
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1703)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-VIII
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  2. A survey on differentiability of six operators in relation to probability and statistics

    • R. M. Dudley, R. NorvaiĊĦa
    Pages 1-72

  3. Product integrals, young integrals and p-variation

    • R. M. Dudley, R. NorvaiĊĦa
    Pages 73-208

  4. Differentiability of the composition and quantile operators for regulated and A. E. continuous functions

    • R. M. Dudley, R. NorvaiĊĦa
    Pages 209-240

  5. Bibliographies on p-variation and ϕ-variation

    • R. M. Dudley, R. NorvaiĊĦa, Jinghua Qian
    Pages 241-272

  6. Back Matter

    Pages 273-282
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Differentiability of Six Operators on Nonsmooth Functions and p-Variation

  • Authors: Richard M. Dudley, Rimas NorvaiĊĦa

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0100744

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-65975-4Published: 21 June 1999

  • eBook ISBN: 978-3-540-48814-9Published: 08 December 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 282

  • Topics: Operator Theory, Global Analysis and Analysis on Manifolds, Real Functions

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