Abstract
This paper deals with the so-called Radon inversion problem formulated in the following way: Given a p>0 and a strictly positive function H continuous on the unit circle {partial {mathbb {D}}}, find a function f holomorphic in the unit disc {mathbb {D}} such that int _0^1|f(zt)|^pdt=H(z) for z in {partial {mathbb {D}}}. We prove solvability of the problem under consideration. For p=2, a technical improvement of the main result related to convergence and divergence of certain series of Taylor coefficients is obtained.
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