Fractional Integrals, Potentials, and Radon Transforms
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Fractional Integrals, Potentials, and Radon Transforms

  1. 576 pages
  2. English
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eBook - ePub

Fractional Integrals, Potentials, and Radon Transforms

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About This Book

Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry.Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud's approach and its generalization, leading to wavelet type representations. New to this Edition

  • Two new chapters and a new appendix, related to Radon transforms and harmonic analysis of linear operators commuting with rotations and dilations have been added.
  • Contains new exercises and bibliographical notes along with a thoroughly expanded list of references.

This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis.

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Yes, you can access Fractional Integrals, Potentials, and Radon Transforms by Boris Rubin in PDF and/or ePUB format, as well as other popular books in Matematica & Analisi matematica. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Chapman and Hall/CRC
Year
2024
ISBN
9781040101940
Edition
2
Topic
Matematica
Subtopic
Analisi matematica

Table of contents

  1. Cover Page
  2. Half-Title Page
  3. Series Page
  4. Title Page
  5. Copyright Page
  6. Dedication Page
  7. Contents
  8. Preface to the Second Edition
  9. Preface to the First Edition
  10. Notation and Conventions
  11. 1 Preliminaries
  12. 2 Basics of One-Dimensional Fractional Integration
  13. 3 Comparison of Ranges and Mapping Properties
  14. 4 Local Properties and the Critical Exponent α=1/p
  15. 5 Marchaud's Method
  16. 6 Fractional Integrals and Wavelet Transforms
  17. 7 Potentials on Rn
  18. 8 One-Sided Riesz Potentials
  19. 9 One-Sided Helmholtz Potentials
  20. 10 Ball Fractional Integrals
  21. 11 Fractional Integrals on the Unit Sphere
  22. 12 Fractional Integrals in Integral Geometry
  23. 13 GĂ„rding-Gindikin Integrals and Radon Transforms
  24. A On Operators Commuting with Rotations and Dilations
  25. Notes and Comments
  26. Bibliography
  27. Subject index