On Kadec's 1/4-Theorem and the Stability of Gabor Frames

Abstract

In Appl. Comput. Harmon. Anal.2 (1995), 160-173, Favier and Zalik presented a multivariate version of Kadec's 1/4-theorem. But their result contains an additional condition Bd(L) < 1. In this paper, we show that this condition may be deleted. In fact, we make a straightforward generalization of Kadec's 1/4-theorem for L2[-π,π]d. We also study the stability of Gabor frames and improve some results from Favier and Zalik (Appl. Comput. Harmon. Anal.2 (1995), 160-173). © 1999 Academic Press.