Peter G. Casazza, Ole Christensen, Nigel J. Kalton
Published 1998-11-24Version 1
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.
Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
Unconditional Frames of Translates in $L_p(\mathbb{R}^d)$
Riesz basis of exponentials for a union of cubes in R^{d}
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