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arXiv · 1701.02420

Polynomially Interpolated Legendre Multiplier Sequences

Matthew Chasse·Tamás Forgács·Andrzej Piotrowski
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Abstract

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 also prove that a non-trivial collection of polynomials of a certain form interpolate multiplier sequences for the Legendre basis, and we state conjectures on how to extend these results.

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Matthew Chasse, Tamás Forgács, Andrzej Piotrowski. 2017-01-10. Polynomially Interpolated Legendre Multiplier Sequences. https://arxiv.org/abs/1701.02420

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