Oversampling, Quasi Affine Frames and Wave Packets
نویسندگان
چکیده
In [11], three of the authors obtained a characterization of certain types of reproducing systems. In this work, we apply these results and methods to various affine–like, wave packets and Gabor systems to determine their frame properties. In particular, we study how oversampled systems inherit properties (like the frame bounds) of the original systems. Moreover, our approach allows us to study the phenomenon of oversampling in much greater generality than is found in the literature. AMS Mathematics Subject Classification: 42C15, 42C40.
منابع مشابه
Frames , Wavelets , and Tomography
For Gabor sets, (g; a, b), it is known that (g; a, b) is a frame if and only if (g; 1/b, 1/a) is a Riesz basis for its span. In particular, for every g there is a0 such that for every a < a0, there is a bm = bm(a) > 0 so that for every b < bm, (g; a, b) is a frame, and (g; 1/b, 1/a) is a Riesz basis sequence. In this talk we shall consider a similar problem for wavelet sets (Ψ; a, b). The main ...
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