Connectivity in the set of Gabor frames

In this paper we present a constructive proof that the set of Gabor frames is path-connected in the L2(Rn)-norm. In particular, this result holds for the set of Gabor-Parseval frames as well as for the set of Gabor orthonormal bases. In order to prove this result, we introduce a construction which shows exactly how to modify a Gabor frame or Parseval frame to obtain a new one with the same property. Our technique is a modification of a method used in [Glas. Mat. 38 (58) (2003) 75-98] to study the connectivity of affine Parseval frames.