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
Descripción
Sumario: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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