Wavelets and Quantum Algebras

Details Wavelets and Quantum Algebras Wavelets and Quantum Algebras

2000-03-26

arxiv.org/abs/math-ph/0003033v1

J. Math. Phys. {\bf 39} (1998) 2346

Physics

Mathematical Physics

27 pages Latex, 3 figure ps

Scientific paper

10.1063/1.532292

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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