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arXiv · 1401.4955

An operator based approach to irregular frames of translates

Peter Balazs·Sigrid Heineken
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Abstract

We consider translates of functions in $L^2(\RRd)$ along an irregular set of points. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel sequence or Riesz sequence. We find a representation of the canonical dual of a frame sequence $\{ϕ( \cdot - λ_k)\}_{k\in \ZZ}$ - where $ϕ$ is a bandlimited function - in terms of its Fourier transform.

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Peter Balazs, Sigrid Heineken. 2014-07-16. An operator based approach to irregular frames of translates. https://arxiv.org/abs/1401.4955

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