Frame properties of wave packet systems in $L^2({\mathbb R}^d)$

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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