Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 38173, 12 pages
doi:10.1155/JIA/2006/38173

Explicit bounds of complex exponential frames

Hualiang Zhong,1 André Boivin,2 and Terry M. Peters1

1Imaging Research Laboratories, Robarts Research Institute, 100 Perth Drive, P.O. Box 5015, London N6A 5K8, ON, Canada
2Department of Mathematics, University of Western Ontario, London N6A 5B7, ON, Canada

Received 23 June 2005; Accepted 16 October 2005

Copyright © 2006 Hualiang Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the stability of complex exponential frames {eiλnx} in L2(−γ,γ), γ>0. Specifically, we improve the 1/4-theorem and obtain explicit upper and lower bounds for some complex exponential frames perturbed along the real and imaginary axes, respectively. Two examples are given to show that the bounds are best possible. In addition, the growth of the entire functions of exponential type γ (γ>π) on the integer sequence is estimated.