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The Quarterly Journal of Mathematics Advance Access originally published online on December 6, 2007
The Quarterly Journal of Mathematics 2008 59(1):15-28; doi:10.1093/qmath/ham023
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

METAPLECTIC OPERATORS ON Cn

Hans G. Feichtinger {dagger}

Faculty of Mathematics, University of Vienna, Nordbergstraβe 15, 1090 Vienna, Austria

Michiel Hazewinkel {ddagger}

Centrum voor Wiskunde en Informatica, P.O. Box 94074, 1090GB Amsterdam, The Netherlands

Norbert Kaiblinger§, Ewa Matusiak ¶ and Markus Neuhauser ||

Faculty of Mathematics, University of Vienna, Nordbergstraβe 15, 1090 Vienna, Austria

§ Corresponding author. E-mail: norbert.kaiblinger{at}univie.ac.at

Received 6 February 2006; revised 30 April 2007
  Abstract

The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H(G), defined for a locally compact abelian group G. For G=Rd, H is the usual Heisenberg group. For the case when G is the finite cyclic group Zn, only partial constructions are known. Here we present new results for this case and we obtain an explicit construction of the metaplectic operators on Cn. We also include applications to Gabor frames.

{dagger} E-mail: hans.feichtinger{at}univie.ac.at

{ddagger} E-mail: michiel.hazewinkel{at}cwi.nl

E-mail: ewa.matusiak{at}univie.ac.at

|| E-mail: markus.neuhauser{at}univie.ac.at


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