Fractional Integrals, Potentials, and Radon Transforms

Boris Rubin (Louisiana State University, United States of America)

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English

Chapman & Hall/CRC
14 August 2024

Calculus & mathematical analysis; Geometry; Applied mathematics; Mathematical physics; Computer science

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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.

By: Boris Rubin (Louisiana State University United States of America)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9781032673660
ISBN 10: 1032673664
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 576
Publication Date: 14 August 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

Boris Rubin is a Professor of Mathematics at Louisiana State University in Baton Rouge (LA, USA). His interests include applications of fractional integrals and harmonic analysis to integral geometry. Prof. Rubin is the author of many articles and a book on this subject. He is an Honorary Editor of the journal “Fractional Calculus and Applied Analysis”.