Abstract:
We define frames for a Hilbert space and the operators associated with them. We then turn our attention to Gabor frames and their relationship with the function valued inner product $<f,g>_1(t) =\sum f(t-k)\overline {g(t-k)}$. Next we introduce a Hilbert C* module as a new setting in which to study these systems, as well as some results here which lead us to believe it is a worthwhile endeavor. Finally we motivate our study of these systems by presenting an application to wireless communications that is currently in use.