ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES

S. E. Mkrtchyan

doi:10.46991/PYSU:A/2009.43.1.061

ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES

Authors

S. E. Mkrtchyan Chair of Theory of Functions, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2009.43.1.061

Keywords:

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

Abstract

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

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Published

2009-02-19

How to Cite

Mkrtchyan, S. E. (2009). ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES. Proceedings of the YSU A: Physical and Mathematical Sciences, 43(1 (218), 61–63. https://doi.org/10.46991/PYSU:A/2009.43.1.061