Basis properties of the p,q-sine functions

TL;DR

This paper refines the understanding of the basis properties of p,q-sine functions by improving thresholds, analyzing their coordinate changes, and providing tighter bounds on associated constants, thus filling gaps in the literature.

Contribution

It introduces improved thresholds for basisness, employs Beurling decomposition for coordinate analysis, and refines bounds on the Riesz constant for p,q-sine functions.

Findings

Enhanced thresholds for basisness of p,q-sine functions.

Application of Beurling decomposition to analyze coordinate changes.

Refined bounds on the Riesz constant.

Abstract

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated to this family. These results seal mathematical gaps in the existing literature on the subject.