Inversion formulas in integral geometry in real hyperbolic space

Abstract

This expository article is a brief survey of authors’ results related to inversion of Radon transforms in the n-dimensional real hyperbolic space. The exposition is focused on horospherical and totally geodesic transforms over the corresponding submanifolds of arbitrary fixed dimension d, 1 ≤ d ≤ n − 1. Our main objective is explicit inversion formulas for these transforms on Lp functions and smooth functions with suitable behavior at infinity.

Department(s)

Mathematics

Document Type

Conference Proceeding

Publication Date

1-1-2019

Journal Title

Contemporary Mathematics

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