Time: 9h00, Friday, November 7, 2014

Location: Room 109, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract:  We  study the asymptotic behavior  of a bounded solution of an inhomogeneous delay linear difference equation  in a Banach space by using the spectrum of  bounded sequences. We get a significant extension of excellent results in [1]. A new simple proof is also found for the famous Gelfand spectral radius theorem. Moreover, among other things we  prove that if the spectrum of a bounded sequence $\{x_n\}_n$ is finite then
$x_n=c_1\vartheta_1^n+c_2\vartheta_2^n+cdots+c_k\vartheta_k^n+o(1)$ as $ntoinfty$ where $|\vartheta_1|=|vartheta_2|=\cdots=|\vartheta_k|=1$.