Non-geodesic spherical funk transforms with one and two centers

Authors

M. Agranovsky, Bar-Ilan University
B. Rubin, Louisiana State University

Document Type

Article

Publication Date

1-1-2020

Abstract

We study non-geodesic Funk-type transforms on the unit sphere Sⁿ in Rⁿ⁺¹ associated with cross-sections of Sⁿ by k-dimensional planes passing through an arbitrary fixed point inside the sphere. The main results include injectivity conditions for these transforms, inversion formulas, and connection with geodesic Funk transforms. We also show that, unlike the case of planes through a single common center, the integrals over spherical sections by planes through two distinct centers provide the corresponding reconstruction problem a unique solution.

Publication Source (Journal or Book title)

Operator Theory Advances and Applications

First Page

29

Last Page

52

Recommended Citation

Agranovsky, M., & Rubin, B. (2020). Non-geodesic spherical funk transforms with one and two centers. Operator Theory Advances and Applications, 279, 29-52. https://doi.org/10.1007/978-3-030-44651-2_7