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Leon Ehrenpreis: Some Old Souvenirs Read chapter Read first chapter

2012 | OriginalPaper | Chapter

Deconvolution for the Pompeiu Problem on the Heisenberg Group, I

Authors : Der-Chen Chang, Wayne Eby, Eric Grinberg

Published in: The Mathematical Legacy of Leon Ehrenpreis

Publisher: Springer Milan

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Abstract

We consider variations on the Pompeiu transform for the Heisenberg group H n and focus on cases where the transform is known to be injective; in particular the cases of averages over a sphere and a ball, or two balls of appropriate radii. In these cases we develop a method which provides for the reconstruction of the function f from its integrals.
In addition, we consider these issues in connection with the Weyl calculus and group Fourier transform. We furthermore explore issues of convergence for this method of deconvolution and related issues of size of the Gelfand transform near the zero sets. Finally, given a set of deconvolvers which work for Euclidean space C n , we consider the problem of how to extend the deconvolution to the Heisenberg group, and we provide the extension in special cases.

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previous chapter On Local Injectivity for Generalized Radon Transforms
next chapter Theta Functions Wronskians and Weierstrass Points for Linear Spaces of Meromorphic Functions
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Metadata
Title
Deconvolution for the Pompeiu Problem on the Heisenberg Group, I
Authors
Der-Chen Chang
Wayne Eby
Eric Grinberg
Copyright Year
2012
Publisher
Springer Milan
Book
The Mathematical Legacy of Leon Ehrenpreis

Print ISBN: 978-88-470-1946-1

Electronic ISBN: 978-88-470-1947-8

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-88-470-1947-8_6

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