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Parity of polynomial multiplier sequences for the Chebyshev basis

Andrzej Piotrowski and Joshua Shterenberg

Vol. 16 (2023), No. 4, 689–703
Abstract

We demonstrate that if p [x] and p is not an even function, then {p(k)}k=0 is not a multiplier sequence for the basis of Chebyshev polynomials of the first kind. We also give a characterization of geometric multiplier sequences for the Chebyshev basis.

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Keywords
multiplier sequences, Chebyshev polynomials, zeros of polynomials, hyperbolic polynomials, linear operators
Mathematical Subject Classification
Primary: 30C15
Milestones
Received: 30 June 2022
Revised: 5 October 2022
Accepted: 10 October 2022
Published: 31 October 2023

Communicated by Michael Dorff
Authors
Andrzej Piotrowski
University of Alaska Southeast
Juneau, AK
United States
Joshua Shterenberg
Boston University
Boston, MA
United States