Regularity Properties of Functional Equations in Several Variables

  • Antal Járai

Part of the Advances in Mathematics book series (ADMA, volume 8)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pages 1-51
  3. Pages 231-334
  4. Back Matter
    Pages 335-363

About this book

Introduction

This book is about regularity properties of functional equations. In the second part of his fifth problem, Hilbert asked, concerning functional equations, "In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumption?” This book contains, in a unified fashion, most of the modern results about regularity of non-composite functional equations with several variables. These results show that "weak” regularity properties, say measurability or continuity, of solutions imply that they are in C[infinity], and hence the equation can be reduced to a differential equation. A long introduction highlights the basic ideas for beginners. Several applications are also included.

Audience

This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics.

Keywords

Manifold differential equation equation function functional equation theorem variable

Authors and affiliations

  • Antal Járai
    • 1
  1. 1.Eötvös Loránd UniversityBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/b105379
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-24413-6
  • Online ISBN 978-0-387-24414-3
  • About this book
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