Abstract
Extending work by Hernandez, Labate and Weiss, we present a sufficent condition for a generalized shift-invariant system to be a Bessel sequence or even a frame for \(L^2({\mathbb R}^d)\). In particular, this leads to a sufficient condition for a wave packet system to form a frame. On the other hand, we show that certain natural conditions on the parameters of such a system exclude the frame property.
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Communicated by Juan Manuel Peña.
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Christensen, O., Rahimi, A. Frame properties of wave packet systems in \(L^2({\mathbb R}^d)\) . Adv Comput Math 29, 101–111 (2008). https://doi.org/10.1007/s10444-007-9038-3
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DOI: https://doi.org/10.1007/s10444-007-9038-3