International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1855-1866
doi:10.1155/S0161171203201034
On a certain class of nonstationary sequences in Hilbert space
Berrabah Bendoukha
Department of Mathematics, University of Mostaganem, Mostaganem 27000, Algeria
Abstract
We study the functions of correlation K(n,m)=〈X(n),X(m)〉 of certain sequences: X(n)=Tnx0, x0∈H where T is a contraction in Hilbert space H. By using the spectral methods of the nonunitary operators we give the general form of K(n,m) and its asymptotic behaviour limp→+∞ K(n+p,m+p).