Wavelets with composite dilations.
Guo, Kanghui; Labate, Demetrio; Lim, Wang-Q; Weiss, Guido; Wilson, Edward — 2004
Electronic Research Announcements of the American Mathematical Society [electronic only]
Wavelets with composite dilations.
The theory of reproducing systems on locally compact abelian groups
A reproducing system is a countable collection of functions such that a general function f can be decomposed as , with some control on the analyzing coefficients . Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G)....
Some remarks on the unified characterization of reproducing systems.
The affine systems generated by Ψ ⊂ L2(Rn) are the systems AA(Ψ) = {Dj A Tk Ψ : j ∈ Z, k ∈ Zn}, where Tk are the translations, and DA the dilations with respect to an invertible matrix A. As shown in [5], there is a simple characterization for those affine systems that are a Parseval...
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