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Completeness of Orthonormal Wavelet Systems for Arbitrary Real Dilations

✍ Scribed by Richard S. Laugesen

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 174 KB
Volume: 11
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.2001.0365

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✦ Synopsis

It is shown that the discrete Calderón condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations. That is, if a > 1, b > 0, and the system = {a j/2 ψ(a j xbk)

A new proof of the Second Oversampling Theorem is found, by similar methods.

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Orthonormal Wavelets and Tight Frames with Arbitrary Real Dilations

✍ Charles K Chui; Xianliang Shi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 170 KB

The objective of this paper is to establish a complete characterization of tight frames, and particularly of orthonormal wavelets, for an arbitrary dilation factor a > 1, that are generated by a family of finitely many functions in L 2 := L 2 (R). This is a generalization of the fundamental work of