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Square-integrability modulo a subgroup


Authors: G. Cassinelli and E. De Vito
Journal: Trans. Amer. Math. Soc. 355 (2003), 1443-1465
MSC (2000): Primary 43A32, 43A85, 42C40
DOI: https://doi.org/10.1090/S0002-9947-02-03220-8
Published electronically: December 4, 2002
MathSciNet review: 1946399
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Abstract: We prove a weak form of the Frobenius reciprocity theorem for locally compact groups. As a consequence, we propose a definition of square-integrable representation modulo a subgroup that clarifies the relations between coherent states, wavelet transforms and covariant localisation observables. A self-contained proof of the imprimitivity theorem for covariant positive operator-valued measures is given.


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Additional Information

G. Cassinelli
Affiliation: Dipartimento di Fisica, Università di Genova, I.N.F.N., Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
Email: cassinelli@genova.infn.it

E. De Vito
Affiliation: Dipartimento di Matematica, Università di Modena, Via Campi 213/B, 41100 Modena, Italy and I.N.F.N., Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
Email: devito@unimo.it

DOI: https://doi.org/10.1090/S0002-9947-02-03220-8
Keywords: Square-integrable representation, frame, localisation observable
Received by editor(s): November 15, 2001
Received by editor(s) in revised form: October 11, 2002
Published electronically: December 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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