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

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

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.

DOI: 10.46991/PYSUA.2009.43.1.061 Physical and Mathematical Sciences, 43(1 (218) 61-63

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Keywords

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

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