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

S. E. Mkrtchyan

doi:10.46991/PYSUA.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/PYSUA.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

Issue

Vol. 43 No. 1 (218) (2009)

Section

Short Communications

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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/PYSUA.2009.43.1.061