Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607784 | Journal of Approximation Theory | 2009 | 16 Pages |
Abstract
It is known that wavelet frames do not exhibit a Nyquist density. Even so, this paper shows that the affine densities of the sets U×VU×V and S×TS×T affect the frame properties of {u−12f(xu−v)}u∈U,v∈V and {s−12g(xs−t)}s∈S,t∈T. In particular, it is shown that there is a relationship between the densities of the dilation sets UU and SS and weighted admissibility constants of ff and gg. This relationship implies a comparison theorem, whereby the affine densities of U×VU×V and S×TS×T are proportional, with proportionality constant depending on the frame bounds and the admissibility constants of ff and gg. These results are also extended to wavelet frame sequences.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Shannon Bishop,