ZAK TRANSFORM FOR BOEHMIANS

It is known that the classical Zak Transform is a linear unitary transformation from L2(R) onto L2 (Q) whose image can be completely characterized. In this paper, we shall construct a Boehmian space B1 containing L2(R) and another Boehmian space B2 containing L2 (Q) and define Zak transform as a continuous linear map of B1 onto B2. We shall also prove that this extended definition is consistent with the classical definition and that there are Boehmains which are not L2 ? functions but for which we can define the generalized Zak transform.