An operator based approach to irregular frames of translates

2014/01/20 by Balazs, Peter, Heineken, Sigrid
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.4955

Abstract

We consider translates of functions in L²(\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( ⋅ - λ_k)\_{k∈ \ZZ} - where ϕ is a bandlimited function - in terms of its Fourier transform.

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