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Radon transforms and Gegenbauer–Chebyshev integrals, I

Radon transforms and Gegenbauer–Chebyshev integrals, I We suggest new modifications of the Helgason’s support theorem and description of the kernel for the hyperplane Radon transform and its dual. The assumptions for functions are formulated in integral terms and close to minimal. The proofs rely on the properties of the Gegenbauer–Chebyshev integrals which generalize Abel type fractional integrals on the positive half-line. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Radon transforms and Gegenbauer–Chebyshev integrals, I

Analysis and Mathematical Physics , Volume 7 (2) – Apr 22, 2016

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-016-0133-9
Publisher site
See Article on Publisher Site

Abstract

We suggest new modifications of the Helgason’s support theorem and description of the kernel for the hyperplane Radon transform and its dual. The assumptions for functions are formulated in integral terms and close to minimal. The proofs rely on the properties of the Gegenbauer–Chebyshev integrals which generalize Abel type fractional integrals on the positive half-line.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Apr 22, 2016

References