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arXiv · 1405.3682

Suffridge's convolution theorem for polynomials with zeros in the unit disk

Martin Lamprecht
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Abstract

In 1976 Suffridge proved an intruiging theorem regarding the convolution of polynomials with zeros only on the unit circle. His result generalizes a special case of the fundamental Grace-Szegö convolution theorem, but so far it is an open problem whether there is a Suffridge-like extension of the general Grace-Szegö convolution theorem. In this paper we try to approach this question from two different directions: First, we show that Suffridge's convolution theorem holds for a certain class of polynomials with zeros in the unit disk and thus obtain an extension of one further special case of the Grace-Szegö convolution theorem. Second, we present non-circular zero domains which stay invariant under the Grace-Szegö convolution hoping that this will lead to further analogs of Suffridge's convolution theorem.

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Martin Lamprecht. 2014-05-14. Suffridge's convolution theorem for polynomials with zeros in the unit disk. https://arxiv.org/abs/1405.3682

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