Open AccessRemarks on the general Funk transform and thermoacoustic tomography
Author(s) -
Victor Palamodov
Publication year - 2010
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2010.4.693
Subject(s) - funk , reciprocal , mathematics , mathematical analysis , computer science , acoustics , physics , philosophy , linguistics
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.
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