The Radon Inversion Problem for Holomorphic Functions in the Unit Disc

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 ∂ D , find a function f holomorphic in the unit disc D such that ∫ 0 1 | f ( z t ) | p d t = H ( z ) for z ∈ ∂ D . We prove s...

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Bibliographic Details
Published in:Computational methods and function theory 2022-03, Vol.22 (1), p.135-156
Main Authors: Kot, P., Pierzchała, P.
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Computational Mathematics and Numerical Analysis
Continuity (mathematics)
Divergence
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Radon
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Summary: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 ∂ D , find a function f holomorphic in the unit disc D such that ∫ 0 1 | f ( z t ) | p d t = H ( z ) for z ∈ ∂ 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.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-021-00379-4