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Continuous Nowhere Differentiable Functions

The Monsters of Analysis

  • Marek Jarnicki
  • Peter Pflug

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Marek Jarnicki, Peter Pflug
    Pages 1-6
  3. Classical Results

    1. Front Matter
      Pages 7-7
    2. Marek Jarnicki, Peter Pflug
      Pages 9-17
    3. Marek Jarnicki, Peter Pflug
      Pages 19-49
    4. Marek Jarnicki, Peter Pflug
      Pages 51-63
    5. Marek Jarnicki, Peter Pflug
      Pages 65-97
    6. Marek Jarnicki, Peter Pflug
      Pages 99-104
  4. Topological Methods

    1. Front Matter
      Pages 105-105
    2. Marek Jarnicki, Peter Pflug
      Pages 107-130
  5. Modern Approach

    1. Front Matter
      Pages 131-131
    2. Marek Jarnicki, Peter Pflug
      Pages 133-186
    3. Marek Jarnicki, Peter Pflug
      Pages 187-201
    4. Marek Jarnicki, Peter Pflug
      Pages 203-208
    5. Marek Jarnicki, Peter Pflug
      Pages 209-244
    6. Marek Jarnicki, Peter Pflug
      Pages 245-254
  6. Riemann Function

    1. Front Matter
      Pages 255-255
    2. Marek Jarnicki, Peter Pflug
      Pages 257-264
  7. Marek Jarnicki, Peter Pflug
    Pages E1-E1
  8. Back Matter
    Pages 265-299

About this book

Introduction

This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann’s continuous, and purportedly nowhere differentiable, function.

For the reader’s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of s

ymbols, problems, and figures enhance the book’s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods.

Keywords

Banach–Jarnik–Mazurkiewicz theorem Johnsen's theorem Weierstrass function lacunary series nondifferentiable functions

Authors and affiliations

  • Marek Jarnicki
    • 1
  • Peter Pflug
    • 2
  1. 1.Institute of MathematicsJagiellonian UniversityKrakówPoland
  2. 2.Insitute for MathematicsCarl von Ossietzky University OldenburgOldenburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-12670-8
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-12669-2
  • Online ISBN 978-3-319-12670-8
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site