Let ( P , V ) be an irreducible imprimitivity system for a group H based on a dualgroup Aˆ of an Abelian group A and acting on a Hilbert spaceH. Given H, wefind necessary and sufficient conditions in order that the set of vectors be a frame inH. Moreover, we apply theseresults to some examples that are considered in the literature in the context ofsquare-integrability modulo a coset space.
Frames from imprimitivity systems
CASSINELLI, GIOVANNI;DE VITO, ERNESTO;
1999-01-01
Abstract
Let ( P , V ) be an irreducible imprimitivity system for a group H based on a dualgroup Aˆ of an Abelian group A and acting on a Hilbert spaceH. Given H, wefind necessary and sufficient conditions in order that the set of vectors be a frame inH. Moreover, we apply theseresults to some examples that are considered in the literature in the context ofsquare-integrability modulo a coset space.
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