Analysis of the affine transformations of the time-frequency plane (Q2721590)

The authors examine reproducing formulas coming from restrictions of the extended metaplectic representation and commutative von Neumann algebras generated by the value of the extended metaplectic representation on one-parameter subgroups. They consider two aspects of the action of the extended metaplectic representation of the group \(G\) to affine, measure and orientation preserving maps of the time-frequency plane on \(L^2\) functions on the line. The paper lists, up to equivalence, all possible reproducing formulas arising by restricting the representation to connected Lie subgroups of \(G\).