The Finite Heisenberg-Weyl Groups in Radar and Communications

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

A Necessary Condition for Weyl-Heisenberg Frames

Unitary Representations of the Canonical Group , the Semi - Direct Product of the Unitary and Weyl - Heisenberg Group : ! ! 1 , 3 " ! " !

The unitary representations of the Canonical group that is defined to be the semidirect product of the unitary group with the Weyl-Heisenberg group, !!1, 3" ! "!1, 3""s #!1, 3" are studied. The Canonical group is equivalently written as the semi-direct product of the special unitary group with the Oscillator group !!1, 3" ! $"!1, 3""s %&!1, 3" . The non-abelian Weyl-Heisenberg group represents ...

Tight Weyl-Heisenberg frames in l2(Z)

Tight Weyl–Heisenberg frames in `(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time–frequency plane is not attainable unless some redundancy is introduced. That is the reason for consideri...

Translation invariant surfaces in the 3-dimensional Heisenberg‎ ‎group

‎In this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm Nil_3$‎ ‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎, ‎where $Delta$ is the Laplacian operator of the surface and $A$‎ ‎is a $3 times 3$-real matrix‎.