Multiplier Sequences for Simple Sets of Polynomials

TL;DR

This paper characterizes simple sets of polynomials whose multiplier sequences include all classical multiplier sequences, providing new insights into the structure and partitioning of multiplier sequences across different polynomial sets.

Contribution

It introduces a new characterization of simple polynomial sets with universal multiplier sequence properties, advancing understanding of multiplier sequence structures.

Findings

Characterization of sequences that are multiplier for all simple polynomial sets

Results towards partitioning classical multiplier sequences

Identification of conditions for universal multiplier sequences

Abstract

In this paper we give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequence for every simple set Q. We characterize sequences of real numbers which are multiplier sequences for every simple set Q, and obtain some results toward the partitioning of the set of classical multiplier sequences.