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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Square-integrability modulo a subgroup
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by G. Cassinelli and E. De Vito PDF
Trans. Amer. Math. Soc. 355 (2003), 1443-1465 Request permission

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
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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
  • Received by editor(s): November 15, 2001
  • Received by editor(s) in revised form: October 11, 2002
  • Published electronically: December 4, 2002
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1946399