Radon Inversion Problem for Holomorphic Functions on Circular, Strictly Convex Domains

In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with C 2 boundary. We show that given p > 0 and a strictly positive, continuous function Φ on ∂ Ω , by use of homogeneous polynomials it is possible to construct a holomorphic function f ∈ O...

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Bibliographic Details
Published in:Complex analysis and operator theory Vol. 15; no. 4
Main Authors: Pierzchała, P., Kot, P.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2021
Springer Nature B.V
Subjects:
Analysis
Analytic functions
Continuity (mathematics)
Domains
Mathematical analysis
Mathematics
Mathematics and Statistics
Operator Theory
Polynomials
Radon
Divergent Taylor series
Radon inversion problem
Inner functions
Secondary 32A0
Boundary behaviour of holomorphic functions of several complex variables
Primary 32A40
ISSN:1661-8254, 1661-8262
Online Access:Get full text
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Summary:In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with C 2 boundary. We show that given p > 0 and a strictly positive, continuous function Φ on ∂ Ω , by use of homogeneous polynomials it is possible to construct a holomorphic function f ∈ O ( Ω ) such that ∫ 0 1 | f ( z t ) | p d t = Φ ( z ) for all z ∈ ∂ Ω . In our approach we make use of so-called lacunary K -summing polynomials (see definition below) that allow us to construct solutions with in some sense extremal properties.
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ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-021-01130-6