Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 38173, 12 pages
Explicit bounds of complex exponential frames
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.
We discuss the stability of complex exponential frames
in , . Specifically, we improve the -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 on the integer sequence is estimated.