L. N. Lyakhov, M. G. Lapshina, “An analog of the Paley–Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2021, Volume 193,Pages 104

An analog of the Paley–Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$

L. N. Lyakhov^a, M. G. Lapshina^b

^a Voronezh State University
^b Lipetsk State Pedagogical University

Abstract: The study of the Radon transformation based on weighted plane waves was initiated by I. A. Kipriyanov. In this paper, we obtain necessary and sufficient conditions satisfied by the Radon $K_\gamma$-transform of smooth functions that decrease together with all their derivatives.

Keywords: Paley–Wiener theorem, Radon transform, Radon–Kipriyanov transform, inversion of the Radon transform, inversion of the Radon–Kipriyanov transform.

UDC: 517.44

MSC: 44A12, 42A38

DOI: 10.36535/0233-6723-2021-193-104-109