Non-geodesic spherical funk transforms with one and two centers

M. Agranovsky, B. Rubin

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations

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.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer
Pages29-52
Number of pages24
DOIs
StatePublished - 2020

Publication series

NameOperator Theory: Advances and Applications
Volume279
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2020.

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