Remarks on the general
Funk transform and thermoacoustic tomography
Victor Palamodov - School of Mathematical Sciences, Tel Aviv University, Ramat Aviv Tel Aviv 69978, Israel (email)
Abstract: We discuss properties of a generalized Minkowski-Funk transform defined for a family of hypersurfaces. We prove two-side estimates and show that the range conditions can be written in terms of the reciprocal Funk transform. Some applications to the spherical mean transform are considered.
Keywords: Funk transform of a density, conjugate points, reciprocal Funk transform, elliptic PDO, range conditions, thermoacoustic tomography, partial scan, Kaczmarz method.
Received: June 2009; Available Online: September 2010.
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