We improve the currently known thresholds for basisness of the family of periodically dilated ,-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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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4309129 | PMC |
| http://dx.doi.org/10.1098/rspa.2014.0642 | DOI Listing |
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