Basis properties of the p, q-sine functions

Lyonell Boulton; Gabriel J. Lord

doi:10.1098/rspa.2014.0642

Basis properties of the p, q-sine functions

Lyonell Boulton^*, Gabriel J. Lord

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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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 with this family. These results seal mathematical gaps in the existing literature on the subject.

Original language	English
Article number	20140642
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	471
Issue number	2175
DOIs	https://doi.org/10.1098/rspa.2014.0642
Publication status	Published - 15 Feb 2015

Keywords

Generalized trigonometric functions
Riesz basis
Schauder basis

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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Cite this

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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 with this family. These results seal mathematical gaps in the existing literature on the subject.",

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AU - Lord, Gabriel J.

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AB - 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 with this family. These results seal mathematical gaps in the existing literature on the subject.

KW - Generalized trigonometric functions

KW - Riesz basis

KW - Schauder basis

U2 - 10.1098/rspa.2014.0642

DO - 10.1098/rspa.2014.0642

M3 - Article

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AN - SCOPUS:84921793043

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Basis properties of the p, q-sine functions

Abstract

Keywords

ASJC Scopus subject areas

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