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arXiv · 2206.14405

Parity of Polynomial Multiplier Sequences for the Chebyshev Basis

Andrzej Piotrowski·Joshua Shterenberg
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Abstract

We demonstrate that if $p\in\mathbb{R}[x]$ and $p$ is not an even function, then $\{p(k)\}^{\infty}_{k=0}$ 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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Andrzej Piotrowski, Joshua Shterenberg. 2022-06-29. Parity of Polynomial Multiplier Sequences for the Chebyshev Basis. https://doi.org/10.2140/involve.2023.16.689

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