Abstract
AbstractIn this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with $${\mathcal {C}}^2$$
C
2
boundary. We show that given $$p>0$$
p
>
0
and a strictly positive, continuous function $$\Phi $$
Φ
on $$\partial \Omega $$
∂
Ω
, by use of homogeneous polynomials it is possible to construct a holomorphic function $$f \in {\mathcal {O}}(\Omega )$$
f
∈
O
(
Ω
)
such that $$\displaystyle \smallint _0^1 |f(zt)|^pdt = \Phi (z)$$
∫
0
1
|
f
(
z
t
)
|
p
d
t
=
Φ
(
z
)
for all $$z \in \partial \Omega $$
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics
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