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  • © 1999

Differentiability of Six Operators on Nonsmooth Functions and p-Variation

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
  2. Product integrals, young integrals and p-variation

    • R. M. Dudley, R. Norvaiša
    Pages 73-208
  3. Bibliographies on p-variation and ϕ-variation

    • R. M. Dudley, R. Norvaiša, Jinghua Qian
    Pages 241-272
  4. Back Matter

    Pages 273-282

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.

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: Richard M. Dudley, Rimas Norvaiša

  • 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

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 52.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions