Communications
Mathematics

On uniqueness of holomorphic and bounded outside the closed logarithmic sector functions representable by lacunary power series

S. E. Mkrtchyan

Chair of Theory of Functions YSU, Armenia

Abstract: In the present note it is shown that for a set of positive integers $\Lambda$ a Müntz- type condition holds if and only if there exists a lacunary power series $f(z)=\displaystyle\sum_{v\in\Lambda}f_v/z^v$ that allows an analytic and bounded continuation to the complement of a closed logarithmical sector with vertex at the origin.

Keywords: closed logarithmic sector, lacunary power series, coefficient function method, analytic continuation.

Received: 05.12.2008
Accepted: 15.01.2009

Language: English