Wenchang Sun
Density of Wavelet Frames
Preprint series: ESI preprints

MSC:

42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

65T20 Discrete and fast Fourier transforms

Abstract: Density conditions for wavelet systems with arbitrary sampling points
to be frames are studied. We show that for a wavelet system generated by admissible
functions and irregular affine lattices to be a frame,
the sampling points must have a positive lower Beurling density.
The same is true for wavelet systems with arbitrary sampling points and nice generating functions.

Keywords: Wavelet frames, affine Beurling density