Ten lectures on wavelets
Inequalities of Littlewood-Paley type for frames and wavelets
SIAM Journal on Mathematical Analysis
The Homogeneous Approximation Property for wavelet frames
Journal of Approximation Theory
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
Duals of Weighted Exponential Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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It is known that wavelet frames do not exhibit a Nyquist density. Even so, this paper shows that the affine densities of the sets UxV and SxT affect the frame properties of {u^-^1^2f(xu-v)}"u"@?"U","v"@?"V and {s^-^1^2g(xs-t)}"s"@?"S","t"@?"T. In particular, it is shown that there is a relationship between the densities of the dilation sets U and S and weighted admissibility constants of f and g. This relationship implies a comparison theorem, whereby the affine densities of UxV and SxT are proportional, with proportionality constant depending on the frame bounds and the admissibility constants of f and g. These results are also extended to wavelet frame sequences.