Radon Inversion Problem for Holomorphic Functions on Circular, Strictly Convex Domains - Pierzchała, P.; Kot, P. (Complex analysis and operator theory, 2021)
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.