Title

Wavelets and quantum algebras

Document Type

Article

Publication Date

1-1-1998

Abstract

Wavelets, known to be useful in nonlinear multiscale processes and in multiresolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators associate to any scaling equation a nonlinear, two parameter algebra. This structure can be mapped onto the quantum group slq(2) in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding nonlinear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail. © 1998 American Institute of Physics.

Publication Source (Journal or Book title)

Journal of Mathematical Physics

First Page

2346

Last Page

2361

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