Frames of translates
Functional Analysis
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/9811144,
title = {Frames of translates},
author = {Peter G. Casazza and Ole Christensen and Nigel J. Kalton},
journal= {arXiv preprint arXiv:math/9811144},
year = {2007}
}
Comments
23 pages