On Laurent series with multiply positive coefficients

Abstract

We consider the class of doubly infinite sequences {a k} k ∞= -∞ whose truncated sequences {a k} n k= -n are 3-times positive in the sense of Pólya and Fekete for all n = 1, 2, ..., and a 0 ≠ 0. We obtain a characterization of this class in terms of independent parameters. We also find an estimate of the growth order of the corresponding Laurent series ∑ k= -∞ ∞akz k. © 2004 Akadémiai Kiadó.