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Regularity Properties of Functional Equations in Several Variables

  • Book
  • © 2005

Overview

Authors:
  1. Antal Járai

    1. Eötvös Loránd University, Budapest, Hungary

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  • Illustrates the basic ideas of regularity properties of functional equations by simple examples, then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion
  • Contains several applications, including very recent ones
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Preliminaries

    Pages 1-51

  3. Steinhaus Type Theorems

    Pages 53-71

  4. Boundedness and Continuity of Solutions

    Pages 73-108

  5. Differentiability and Analyticity

    Pages 109-155

  6. Regularity Theorems on Manifolds

    Pages 157-167

  7. Regularity Results with Fewer Variables

    Pages 169-229

  8. Applications

    Pages 231-334

  9. Back Matter

    Pages 335-363
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Keywords

About this book

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.

Reviews

From the reviews of the first edition:

"This book is a welcome addition to the functional equations literature. … The author does a masterful job of organizing and summarizing the results of the last 50 years and weaving them together into a coherent general theory. There are over 200 references. The book is very carefully written … . The author has certainly achieved his stated goal of making these results ‘more accessible and easier to use for everyone working with functional equations.’" (Bruce Ebanks, Zentralblatt MATH, Vol. 1081, 2006)

Authors and Affiliations

  • Eötvös Loránd University, Budapest, Hungary

    Antal Járai

Bibliographic Information

  • Book Title: Regularity Properties of Functional Equations in Several Variables

  • Authors: Antal Járai

  • Series Title: Advances in Mathematics

  • DOI: https://doi.org/10.1007/b105379

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag US 2005

  • Hardcover ISBN: 978-0-387-24413-6Published: 03 March 2005

  • Softcover ISBN: 978-1-4419-3740-7Published: 08 December 2010

  • eBook ISBN: 978-0-387-24414-3Published: 30 March 2006

  • Edition Number: 1

  • Number of Pages: IX, 363

  • Topics: Difference and Functional Equations

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