Parity of polynomial multiplier sequences for the Chebyshev basis

Piotrowski, Andrzej; Shterenberg, Joshua

doi:10.2140/involve.2023.16.689

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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

DOI: 10.2140/involve.2023.16.689

Abstract

We demonstrate that if $p \in ℝ [x]$ and $p$ is not an even function, then ${p (k)}_{k = 0}^{\infty}$ 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.

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

Vol. 16, No. 4, 2023