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Square-integrability modulo a subgroup
Author(s):
G.
Cassinelli;
E.
De Vito
Journal:
Trans. Amer. Math. Soc.
355
(2003),
1443-1465.
MSC (2000):
Primary 43A32, 43A85, 42C40
Posted:
December 4, 2002
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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:
10.1090/S0002-9947-02-03220-8
PII:
S 0002-9947(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
Posted:
December 4, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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