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A symmetric integral identity for Bessel functions with applications to integral geometry

A symmetric integral identity for Bessel functions with applications to integral geometry In the article of Kunyansky (Inverse Probl 23(1):373–383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in $${\mathbb {R}}^{n}$$ R n . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in $${\mathbb {R}}^{2}$$ R 2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

A symmetric integral identity for Bessel functions with applications to integral geometry

Analysis and Mathematical Physics , Volume 9 (1) – Dec 20, 2017

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-017-0203-7
Publisher site
See Article on Publisher Site

Abstract

In the article of Kunyansky (Inverse Probl 23(1):373–383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in $${\mathbb {R}}^{n}$$ R n . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in $${\mathbb {R}}^{2}$$ R 2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 20, 2017

References