EXPLICIT BOUNDS OF COMPLEX EXPONENTIAL FRAMES

We discuss the stability of complex exponential frames {eiλnx} in L2(−γ,γ), γ> 0. Specif-ically, 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. 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. 1