Open Access

Explicit bounds of complex exponential frames

Journal of Inequalities and Applications20062006:38173

DOI: 10.1155/JIA/2006/38173

Received: 23 June 2005

Accepted: 16 October 2005

Published: 2 May 2006

Abstract

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.

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Authors’ Affiliations

(1)
Imaging Research Laboratories, Robarts Research Institute
(2)
Department of Mathematics, University of Western Ontario

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Copyright

© Hualiang Zhong et al. 2006

This article is published under license to BioMed Central Ltd. 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.