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Analysis of the affine transformations of the time-frequency plane

Published online by Cambridge University Press:  17 April 2009

Filippo De Mari  and
Krzysztof Nowak
Filippo De Mari
Affiliation:
DIMET, Piazzale J. F. Kennedy, Pad. D, 16129 Genova, Italy e-mail: [email protected]
Krzysztof Nowak
Affiliation:
Purchase College, 735 Anderson Hill Rd.Purchase, NY 10577–1400United States of America e-mail: [email protected]
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Abstract

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We consider two aspects of the action of the extended metaplectic representation of the group G of affine, measure and orientation preserving maps of the time-frequency plane on L2 functions on the line. On the one hand, we list, up to equivalence, all possible reproducing formulas that arise by restricting the representation to connected Lie subgroups of G. On the other hand, we describe, in terms of Weyl calculus, the commutative von Neumann algebras generated by restriction to one-parameter subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 195 - 218
Copyright
Copyright © Australian Mathematical Society 2001

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