Coherent state lattices and square integrability of representations
(2003) Journal of Physics A: Mathematical and General — Vol. 36, n° 47, p. 11817-11835 (2003)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- In this paper, we discretize the continuous theory of coherent states on a general semidirect product group G = V x S, where V is a vector space and S subset of GL(V) is a semisimple connected Lie group. We show that it is always possible to construct a discrete frame associated with a unitary irreducible representation of G, which is square integrable modulo an affine admissible section. We also prove the converse result that the existence of a discrete frame associated with a unitary representation U of G, indexed by a homogeneous space Gamma, implies the square integrability of U on Gamma.
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Citations
Hohouéto, A., Thirulagasanthar, K., Ali, ST., & Antoine, J.-P. (2003). Coherent state lattices and square integrability of representations. Journal of Physics A: Mathematical and General, 36(47), 11817-11835. https://hdl.handle.net/2078.5/24655 (Original work published 2003)