Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605124 | Applied and Computational Harmonic Analysis | 2015 | 18 Pages |
Abstract
We construct a continuous wavelet transform (CWT) on the torus T2T2 following a group-theoretical approach based on the conformal group SO(2,2)SO(2,2). The Euclidean limit reproduces wavelets on the plane R2R2 with two dilations, which can be defined through the natural tensor product representation of usual wavelets on RR. Restricting ourselves to a single dilation imposes severe conditions for the mother wavelet that can be overcome by adding extra modular group SL(2,Z)SL(2,Z) transformations, thus leading to the concept of modular wavelets. We define modular-admissible functions and prove frame conditions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Manuel Calixto, Julio Guerrero, Daniela Roşca,