Excesses of Gabor frames

A Gabor system for L-2(R-d) has the form G(g, Lambda) = {e(2piibx)g(x - a)}((a,b)is an element ofLambda), where g is an element of L-2(R-d) and Lambda is a sequence of points in R-2d. We prove that, with only a mild restriction on the generator g and for nearly arbitrary sets of time-frequency shifts Lambda, an overcomplete Gabor frame has infinite excess, and in fact there exists an infinite subset that can be removed yet leave a frame. The proof of this result yields an interesting connection between the density of Lambda and the excess of the frame. (C) 2003 Elsevier Science (USA). All rights reserved.