The non-existence of cubic Legendre multiplier sequences

Abstract

The main result in this paper is the proof of the recently conjectured non-existence of cubic Legendre multiplier sequences. We also give an alternative proof of the non-existence of linear Legendre multiplier sequences, using a method that will allow for a more methodical treatment of sequences interpolated by higher degree polynomials.

Several typos were corrected. Sections 2 and 3 were reorganized with added definitions. The appendix was incorporated into the body, the statement and proof of Lemma 4 was corrected. The proofs of Lemma 2 and Theorem 5 were streamlined, and several new references were added

References in corpus (2)

• Polya-Schur master theorems for circular domains and their boundaries
• Multivariate Polya-Schur classification problems in the Weyl algebra

Cited by in corpus (2)

• Multiplier sequences, classes of generalized Bessel functions and open problems
• Parity of Polynomial Multiplier Sequences for the Chebyshev Basis