AffiliationDepartment of Mathematics, University of Arizona
Elementary symmetric polynomials
Generalized Radon transforms
Zeros of symmetric polynomials
MetadataShow full item record
PublisherSpringer Science and Business Media LLC
CitationAmbartsoumian, G., Latifi, M.J. Inversion and Symmetries of the Star Transform. J Geom Anal (2021).
JournalJournal of Geometric Analysis
Rights© Mathematica Josephina, Inc. 2021
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractThe star transform is a generalized Radon transform mapping a function of two variables to its integrals along “star-shaped” trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in mathematical models of various imaging modalities based on scattering of elementary particles. The paper presents a comprehensive study of the inversion of the star transform. We describe the necessary and sufficient conditions for invertibility of the star transform, introduce a new inversion formula and discuss its stability properties. As an unexpected bonus of our approach, we prove a conjecture from algebraic geometry about the zero sets of elementary symmetric polynomials. © 2021, Mathematica Josephina, Inc.
Note12 month embargo; published: 03 May 2021
VersionFinal accepted manuscript
SponsorsNational Science Foundation