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
Ludu, A., Greiner, M., & Draayer, J. (1998). Wavelets and quantum algebras. Journal of Mathematical Physics, 39 (4), 2346-2361. https://doi.org/10.1063/1.532292