Abstract
AbstractThis paper deals with the so-called Radon inversion problem formulated in the following way: Given a $$p>0$$
p
>
0
and a strictly positive function H continuous on the unit circle $${\partial {\mathbb {D}}}$$
∂
D
, find a function f holomorphic in the unit disc $${\mathbb {D}}$$
D
such that $$\int _0^1|f(zt)|^pdt=H(z)$$
∫
0
1
|
f
(
z
t
)
|
p
d
t
=
H
(
z
)
for $$z \in {\partial {\mathbb {D}}}$$
z
∈
∂
D
. We prove solvability of the problem under consideration. For $$p=2$$
p
=
2
, a technical improvement of the main result related to convergence and divergence of certain series of Taylor coefficients is obtained.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Analysis
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