✦ LIBER ✦

Wavelets of Wilson Type with Arbitrary Shapes

✍ Scribed by Charles K. Chui; Xianliang Shi

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 163 KB
Volume: 8
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.2000.0277

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✦ Synopsis

Motivated by the Gaussian bases of Coifman and Meyer and the need of bases with arbitrary shapes which may have to be different at different locations, we derive complete characterizations of window functions and their duals for localization of all appropriate sines and cosines that give rise to biorthogonal Schauder bases, Riesz bases, and frames. In addition, when the window functions are simply integer translates of a single window function, we give an explicit formulation of its dual that generates the biorthogonal basis, regardless of the shape and support of the window function. Besides the Coifman-Meyer Gaussian bases, several other examples of wavelets of Wilson type are given.

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