2009; Physical and Mathematical Sciences, 43(1 (218): 61–63
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ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES

S. E. Mkrtchyan*

Received: 2025-02-28 · Published: 2009-02-19

© 2009 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES
Author
S. E. Mkrtchyan
Published
2009-02-19
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.46991/PYSUA.2009.43.1.061

Abstract

In the present note it is shown that for a set of positive integers ∧ a Müntztype condition holds if and only if there exists a lacunary power series f(z)=∑v∈∧fv/zv that allows an analytic and bounded continuation to the complement of a closed logarithmical sector with vertex at the origin.
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