Square integrability of group-representations on homogeneous spaces .1. Reproducing triples and frames
(1991) Institut Henri Poincare. Annales: Physique Theorique — Vol. 55, n° 4, p. 829-855 (1991)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- A connection between a class of positive operator valued measures on a Hilbert space and certain reproducing kernel Hilbert spaces leads to the concept of a reproducing triple. Any such object generates an overcomplete family of vectors, which has most of the attributes of the familiar coherent states. A particular case of such a triple is the notion of frame, which, in a discrete situation, coincides with the structure underlying nonorthogonal expansions. The abstract machinery developed here will be used in a second paper to give a general definition of a square integrable representation of a group and the associated coherent states.
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Citations
Ali, ST., Antoine, J.-P., & Gazeau, JP. (1991). Square integrability of group-representations on homogeneous spaces .1. Reproducing triples and frames. Institut Henri Poincare. Annales: Physique Theorique, 55(4), 829-855. https://hdl.handle.net/2078.5/27967 (Original work published 1991)