منابع مشابه
Density of Wavelet Frames
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.
متن کاملIrregular wavelet frames on L2(R)
If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...
متن کاملTight wavelet frames for irregular multiresolution analysis
An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of ...
متن کاملOn the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames
We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.
متن کاملGabor Frames over Irregular Lattices
We give necessary and suÆcient conditions for g 2W (L1; `) to generate a Gabor frame over certain irregular lattices.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-04-07410-6