TY - JOUR 
A1 - Guerrero García, Julio
AU - Calixto Molina, Manuel
T1 - Wavelet Transform on the Circle and the Real Line: a Unified Group-Theoretical Treatment
Y1 - 2006
SN - 1063-5203
UR - http://hdl.handle.net/10317/508
UR - arXiv:math-ph/0406057v2
AB - We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle S1 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 L2(X, dx) is described, relating carrier spaces X to (first or higher-order) “polarization subalgebras” PX. We also provide explicit admissibility and continuous frame conditions for wavelets
on S1 and discuss the Euclidean limit in terms of group contraction.
KW - Matemática Aplicada
KW - Transformación Contínua Wavelet
KW - Polarización de Subálgebras
KW - Líneas Reales
KW - Grupo de Tratamiento Teórico
LA - eng
PB - Elsevier
ER -