General Existence Theorems for Orthonormal Wavelets, an Abstract Approach | Zendy

Larry Baggett | Zendy; Alan L. Carey | Zendy; William Moran | Zendy; Peter Ohring | Zendy

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General Existence Theorems for Orthonormal Wavelets, an Abstract Approach

Author(s) -

Larry Baggett,

Alan L. Carey,

William Moran,

Peter Ohring

Publication year - 1995

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195164793

Subject(s) - orthonormal basis , wavelet , mathematics , legendre wavelet , generalization , pure mathematics , multiresolution analysis , noncommutative geometry , mathematical analysis , discrete wavelet transform , wavelet transform , computer science , artificial intelligence , physics , quantum mechanics

Methods from noncommutative harmonic analysis are used to develop an abstract theory of orthonormal wavelets. The relationship between the existence of an orthonormal wavelet and the existence of a multi-resolution is clarified, and four theorems guaranteeing the existence of wavelets are proved. As a special case of the fourth theorem, a generalization of known results on the existence of smooth wavelets having compact support is obtained.

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