
TL;DR
This paper proves that any integrable function on a smooth, star-shaped boundary with zero integral can be realized as the boundary value of an analytic function inside the domain.
Contribution
It establishes a new boundary value representation result for analytic functions on star-shaped domains with smooth boundaries.
Findings
Any zero-mean integrable boundary function is a boundary value of an analytic function.
The result extends boundary value theory for holomorphic functions in star-shaped domains.
Provides a constructive approach to boundary value problems for analytic functions.
Abstract
Let be a connected bounded domain on the complex plane, be its boundary, which is closed, star-shaped, -smooth, and is the set of analytic (holomorphic) in functions. The aim of this paper is to prove that an arbitrary , satisfying the condition , can be boundary value of an .
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Meromorphic and Entire Functions
