This article is cited in 10 papers

The Generalized Radon Transform on the Plane, the Inverse Transform, and the Cavalieri Conditions

D. A. Popov

A. N. Belozersky Institute of Physico-Chemical Biology, M. V. Lomonosov Moscow State University

Abstract: In the two-dimensional case, the generalized Radon transform takes each function supported in a disk to the values of the integrals of that function over a family of curves. We assume that the curves differ only slightly from straight lines and the network formed by these curves has the same topological structure as the network of straight lines. Thus, the generalized Radon transform specifies a function on the set of straight lines. Under these conditions, we obtain a solution of the inversion problem for the generalized Radon transform and indicate a Cavalieri condition describing the range of this transform in the space of functions on the set of straight lines.

UDC: 517.444

Received: 20.03.2001

DOI: 10.4213/faa272

 English version: Functional Analysis and Its Applications, 2001, 35:4, 270–283

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