Remarks on the general Funk transform and thermoacoustic tomography
Open Access
- 1 January 2010
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems & Imaging
- Vol. 4 (4) , 693-702
- https://doi.org/10.3934/ipi.2010.4.693
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
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- The dependence of the generalized Radon transform on defining measuresTransactions of the American Mathematical Society, 1980