Natural Science, Mathematics, 2025
ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES
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Submitted: 2025-02-28; Published: 2025-02-28
Š 2025 by author(s) and The Gufo Inc.
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Abstract
In the present note it is shown that for a set of positive integers â§Â a MĂźntztype condition holds if and only if there exists a lacunary power series f(z)=âvââ§fv/zv that allows an analytic and bounded continuation to the complement of a closed logarithmical sector with vertex at the origin.