This article is cited in 1 paper

The Paley–Wiener Theorem for the Generalized Radon Transform on the Plane

D. A. Popov

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

Abstract: We consider the problem of reconstructing a function on the disk $\mathbb{D}\subset\mathbb{R}^2$ from its integrals over curves close to straight lines, i.e., the inversion problem for the generalized Radon transform. Necessary and sufficient conditions on the range of the generalized Radon transform are obtained for functions supported in a smaller disk $\mathbb{D}'\subset\mathbb{D}$ under the additional condition that the curves that do not meet $\mathbb{D}'$ coincide with the corresponding straight lines.

Keywords: Paley–Winer theorem, Radon transform, Fourier integral operator, Zernike polynomial.

UDC: 517.444

Received: 28.04.2003

DOI: 10.4213/faa158

 English version: Functional Analysis and Its Applications, 2003, 37:3, 215–220

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