Parity of polynomial multiplier sequences for the Chebyshev basis.

Abstract

Abstract. We demonstrate that if p ∈ R[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.