1301.3783 (Davide Barbieri et al.)

Coherent states of the Euclidean Motion group and CR regularity    [PDF]

Davide Barbieri, Giovanna Citti

We show how the coherent states transform associated to the irreducible representations of the Euclidean Motion group can give rise to a reproducing kernel Hilbert space, even if such representations are not square integrable. Once this result is established, we can characterize such Hilbert space for the case of a minimal uncertainty mother wavelet in terms of a complex regularity related to the natural almost complex structure of the group, in strict analogy with the Bargmann transform.

View original: http://arxiv.org/abs/1301.3783