Basis properties of the p, q-sine functions

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 Rie...

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Detalles Bibliográficos
Autores principales: Boulton, Lyonell, Lord, Gabriel J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2015
Materias:
Research Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4309129/
https://www.ncbi.nlm.nih.gov/pubmed/25663809
http://dx.doi.org/10.1098/rspa.2014.0642
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author Boulton, Lyonell
Lord, Gabriel J.
author_facet Boulton, Lyonell
Lord, Gabriel J.
author_sort Boulton, Lyonell
collection PubMed
description 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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spelling pubmed-43091292015-02-08 Basis properties of the p, q-sine functions Boulton, Lyonell Lord, Gabriel J. Proc Math Phys Eng Sci Research Articles 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. The Royal Society Publishing 2015-02-08 /pmc/articles/PMC4309129/ /pubmed/25663809 http://dx.doi.org/10.1098/rspa.2014.0642 Text en http://creativecommons.org/licenses/by/4.0/ © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Research Articles
Boulton, Lyonell
Lord, Gabriel J.
Basis properties of the p, q-sine functions
title Basis properties of the p, q-sine functions
title_full Basis properties of the p, q-sine functions
title_fullStr Basis properties of the p, q-sine functions
title_full_unstemmed Basis properties of the p, q-sine functions
title_short Basis properties of the p, q-sine functions
title_sort basis properties of the p, q-sine functions
topic Research Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4309129/
https://www.ncbi.nlm.nih.gov/pubmed/25663809
http://dx.doi.org/10.1098/rspa.2014.0642
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