Year: 1998
Type: article
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.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.532292
Authors: A. Ludu, M. Greiner, J. P. Draayer
Institutions: Louisiana State University, Technische Universität Dresden
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1991817486