THE FOURIER TRANSFORM APPROACH TO INVERSION OF λ-COSINE AND FUNK TRANSFORMS ON THE UNIT SPHERE

Boris Rubin

doi:10.1090/proc/15948

THE FOURIER TRANSFORM APPROACH TO INVERSION OF λ-COSINE AND FUNK TRANSFORMS ON THE UNIT SPHERE

Boris Rubin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We use the classical Fourier analysis on Rn to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the relevant λ-cosine transforms.

Original language	English
Pages (from-to)	2037-2047
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	5
DOIs	https://doi.org/10.1090/proc/15948
State	Published - 2022
Externally published	Yes

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© 2022 American Mathematical Society. All rights reserved.

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abstract = "We use the classical Fourier analysis on Rn to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the relevant λ-cosine transforms.",

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AB - We use the classical Fourier analysis on Rn to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the relevant λ-cosine transforms.

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THE FOURIER TRANSFORM APPROACH TO INVERSION OF λ-COSINE AND FUNK TRANSFORMS ON THE UNIT SPHERE

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