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November  2010, 4(4): 649-653. doi: 10.3934/ipi.2010.4.649

A remark on the weighted Radon transform on the plane

Simon Gindikin 1,

1. 

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

Received  January 2009 Revised  May 2010 Published  September 2010

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: inversion formula., Radon transform.
Mathematics Subject Classification: 44A1.
Citation: Simon Gindikin. A remark on the weighted Radon transform on the plane. Inverse Problems & Imaging, 2010, 4 (4) : 649-653. doi: 10.3934/ipi.2010.4.649
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.  Google Scholar

[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.  Google Scholar

show all references

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.  Google Scholar

[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.  Google Scholar

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