Estimates, decay properties, and computation of the dual function for Gabor frames (Q1973854)

It is proved that if a function \(g\in L^2(\mathbb R)\) generating a Gabor frame has exponential decay, then the dual function also has exponential decay. A method for approximation of the dual function using finite-dimensional methods is presented; in the case of a dual with exponential decay, an error estimate is given (however, with some unknown constants appearing in the expression). Finally, for splines of order two the region in the time-frequency plane where a frame is generated is estimated numerically.