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

S. E. Mkrtchyan

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Submitted: 2025-02-28; Published: 2009-02-19

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

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

Abstract

Author(s)

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