Extension of holomorphic functions onto a special domain

TL;DR

This paper extends Arakelyan's result by establishing a relationship between the holomorphic extension of functions from the unit disc to a domain excluding a ray and the interpolation of their Taylor coefficients.

Contribution

It introduces a modified version of Arakelyan's theorem linking holomorphic extension properties with Taylor coefficient interpolation on a specific domain.

Findings

Established a new relationship between holomorphic extension and Taylor coefficient interpolation.

Extended Arakelyan's result to a domain excluding a half-line.

Provided a modified theorem applicable to the domain $\,\mathbb C\setminus[1,\infty)$.

Abstract

We present a modified version of the Arakelyan's result: a relationship between holomorphic extension of a holomorphic function on the unit disc onto the domain $\mathbb C\setminus[1,\infty)$ and its Taylor coefficients' interpolation.