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arXiv · 2204.05081

On the analytic functions

Alexander G. Ramm
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Abstract

Let $Ω$ be a connected bounded domain on the complex plane, $S$ be its boundary, which is closed, star-shaped, $C^1$-smooth, and $H(Ω)$ is the set of analytic (holomorphic) in $Ω$ functions. The aim of this paper is to prove that an arbitrary $f\in L^1(S)$, satisfying the condition $\int_Sf(s)ds=0$, can be boundary value of an $f\in H(Ω)$.

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Alexander G. Ramm. 2022-10-04. On the analytic functions. https://arxiv.org/abs/2204.05081

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