Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: December 4, 2002
MathSciNet review: 1946399
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 43A32, 43A85, 42C40

Retrieve articles in all journals with MSC (2000): 43A32, 43A85, 42C40


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: http://dx.doi.org/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
Published electronically: December 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society