Abstract
In 1976, Suffridge proved an intriguing 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 show that Suffridge’s convolution theorem holds for a certain class of polynomials with zeros in the unit disk and thus obtain an extension for one further special case of the Grace–Szegö convolution theorem.
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Communicated by George Csordas.
The author would like to thank the referee for his very thorough review of the paper and for several helpful comments and remarks.
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Lamprecht, M. Suffridge’s Convolution Theorem for Polynomials with Zeros in the Unit Disk. Comput. Methods Funct. Theory 16, 433–455 (2016). https://doi.org/10.1007/s40315-015-0151-x
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DOI: https://doi.org/10.1007/s40315-015-0151-x