P. Boggiatto, C. Fernandez, A. Galbis, A group representation related to the Stockwell transform, Indiana Univ. Math. J. 58 (2009), 2277-2296
Abstract
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We obtain a group structure admitting an irreducible and integrable representation on a Hilbert space with the property that the corresponding wavelet transform coincides with the Stockwell transform.
The group is constructed in a similar way to the Weyl-Heisenberg group but it is not unimodular and it contains the affine group as a subgroup.
The obtained results are coherent with the fact that the Stockwell transform is a hybrid of the Gabor and the wavelet transforms.
P. Boggiatto: Department of Mathematics
University of Torino
Via Carlo Alberto 10
10123 Torino, Italy
C. Fernández, A. Galbis: Departamento de Análisis Matemático
Universidad de Valencia
Doctor Moliner 50
46100 Burjasot (Valencia), Spain
Corresponding author's e-mail address : antonio.galbis@uv.es
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