Wavelet Transform on the Circle and the Real Line: A Unified Group-Theoretical Treatment [article]

Manuel Calixto, Julio Guerrero
2006 arXiv   pre-print
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle S^1 and the real line R, following the general formalism of Coherent States (CS) associated to unitary square integrable (modulo a subgroup, possibly) representations of the group SL(2,R). A general procedure for obtaining unitary representations of a group G of affine transformations on a space of signals L^2(X,dx) is described, relating carrier spaces X to (first or higher-order)
more » ... tion subalgebras" P_X. We also provide explicit admissibility and continuous frame conditions for wavelets on S^1 and discuss the Euclidean limit in terms of group contraction.
arXiv:math-ph/0406057v2 fatcat:v2mujgx7kvg3rphsepudckpbda