Polynomially Interpolated Legendre Multiplier Sequences

Matthew Chasse, Tamás Forgács, Andrzej Piotrowski

We prove that every multiplier sequence for the Legendre basis which can be interpolated by a polynomial has the form $\{h(k^2+k){\}}_{k=0}^{\infty }$, where $h\in \mathbb{R}[x]$. We a…