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Radon transforms and Gegenbauer–Chebyshev integrals, II; examples

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Abstract

We transfer the results of Part I related to the modified support theorem and the kernel description of the hyperplane Radon transform to totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the spherical mean transform for spheres through the origin. The assumptions for functions are formulated in integral terms and close to minimal.

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Notes

  1. The inequality \(f \ne 0\) means that the set \(\{x\in {\mathbb R}^n: f (x)\ne 0\}\) has positive measure.

  2. This problem was solved after the present paper had been submitted. See Theorems 4.2, 5.2, 6.2, and 7.1 in [10].

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Acknowledgments

I am grateful to Emily Ribando-Gros for figures in this paper. She was supported by the NSF VIGRE program.

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  1. Department of Mathematics, 303 Lockett Hall, Louisiana State University, Baton Rouge, LA, 70803, USA

    Boris Rubin

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Rubin, B. Radon transforms and Gegenbauer–Chebyshev integrals, II; examples. Anal.Math.Phys. 7, 349–375 (2017). https://doi.org/10.1007/s13324-016-0145-5

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