On the growth of entire generating functions of multiply positive sequences

O. M. Katkova

Department of Mechanics and Mathematics, V. N. Karazin Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine

Abstract: The paper deals with the class of entire generating functions of $k$-times positive (by Fecete, Pólya, Schoenberg) sequences of coefficients. For all integers $k$, $1\le k<\infty$, we give the exhaustive description of the growth and trigonomertical around zero indicators of the above functions.

MSC: 30D20, 30D15

Received: 24.12.2001

Language: English

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