February Fourier Talks 2010

Jean-Pierre Gabardo


Irregular Gabor systems yielding Parseval frames


Given a window g in L2(Rn), we will discuss the problem of constructing associated irregular Gabor systems forming a Parseval frame for the space L2(Rn). In the particular case where n=1 and g is the hyperbolic secant, we will describe explicitly all the lattices in the time-frequency plane which can used to form a Parseval frame associated with the window g. They are an uncountable number of such lattices and they turn out to be all non-separable.