A remark on the weighted Radon transform on the plane

Simon Gindikin

doi:10.3934/ipi.2010.4.649

Article Contents

2010, Volume 4, Issue 4: 649-653. Doi: 10.3934/ipi.2010.4.649

This issue Previous Article Special functions Next Article The Gauss-Bonnet-Grotemeyer Theorem in space forms

A remark on the weighted Radon transform on the plane

Simon Gindikin^1,

1.
Departm. of Mathematics, Rutgers University, Piscataway, NJ 08854-8019

Received: December 31, 2008

Revised: April 30, 2010

Published: October 2010

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Abstract

We consider a class of weights on the plane for which the weighted Radon transform admits an inversion formula similar to the classical one. These transforms are naturally dual to the attenuated Radon.

Keywords:

Radon transform,
inversion formula.

Mathematics Subject Classification: 44A12.

Citation:

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References

[1]	R. G. Novikov, An inversion formula for the attenuated X-ray transform, Ark. Mat., 40 (2002), 145-167.doi: doi:10.1007/BF02384507.
[2]	I. M. Gelfand, S. G. Gindikin and Z. Ya. Shapiro, A local problem of integral geometry in a space of curves, Funct. Anal. Appl., 13 (1980), 87-102.doi: doi:10.1007/BF01077241.