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 rep- resentation 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.
Analysis of the affine transformations of the time-frequency plane
DE MARI CASARETO DAL VERME, FILIPPO;
2001-01-01
Abstract
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 rep- resentation 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.
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