Basis properties of the p, q-sine functions

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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 languageEnglish
Article number20140642
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume471
Issue number2175
DOIs
Publication statusPublished - 15 Feb 2015

Keywords

  • Generalized trigonometric functions
  • Riesz basis
  • Schauder basis

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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