2013/01/16 by Davide Barbieri, Barbieri, Davide, Giovanna Citti +1
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Representation Theory (math.RT) #math-ph #math.CV #math.GR #math.MP #math.RT
paper · pdf · doi:10.48550/arxiv.1301.3783
arxiv created 2014/03/30 · arxiv updated 2014/04/01
We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the Euclidean Motion SE(2). A natural Hilbert norm for functions on the group is constructed that makes the wavelet transform an isometry, but since the considered representations are not square integrable the resulting Hilbert space will not coincide with L2(SE(2)). The reproducing kernel Hilbert subspace generated by the wavelet transform, for the case of a minimal uncertainty mother wavelet, can be characterized in terms of the complex regularity defined by the natural CR structure of the group. Relations with the Bargmann transform are presented.