Frames of translates

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We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural numbers, then this family is a frame if and only if it is a Riesz basis. We also consider arbitrary sequences of translates and show that for sparse sets, having an upper frame bound is equivalent to the family being a frame sequence. Finally, we use the fractional Hausdorff dimension to identify classes of exact frame sequences.
23 pages

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Functional Analysis, 46C05; 46B20

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http://salesiana.dossiersoluciones.com/handle/123456789/77756

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9811144
 http://arxiv.org/abs/math/9811144

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arXiv