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Wavelets and Quantum Algebras

Andrei Ludu·Martin Greiner·Jerry P. Draayer
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Abstract

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group $su_{q}(2)$ in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding non-linear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail.

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BibTeXRIS

Andrei Ludu, Martin Greiner, Jerry P. Draayer. 2000-03-26. Wavelets and Quantum Algebras. https://doi.org/10.1063/1.532292

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