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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 ofChebyshev polynomials of the first kind. We also give a characterization ofgeometric multiplier sequences for the Chebyshev basis.

Parity of Polynomial Multiplier Sequences for the Chebyshev Basis