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.

中文翻译：

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单位圆盘中全纯函数的Radon反演问题

本文以以下方式处理所谓的Radon反演问题：给定\（p> 0 \）和在单位圆上连续的严格正函数H （{\ partial {\ mathbb {D}}} \） ，找到一个函数˚F全纯单位圆\（{\ mathbb {d}} \），使得\（\ INT _0 ^ 1 | F（ZT）| ^ PDT = H（z）的\）为\（ z \ in {\ partial {\ mathbb {D}}} \）中。我们证明了所考虑问题的可解决性。对于\（p = 2 \），可以获得与某些泰勒系数级数的收敛和发散有关的主要结果的技术改进。