Riesz Bases in Subspaces of L2 (R+ )

Abstract.

In a recent investigation [8] concerning the asymptotic behavior of Gram—Schmidt orthonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in $L_2$({\bf R}$_+)$ arose. In this paper, we provide a sufficient condition to determine whether the nonnegative translates form a Riesz system on $L_2$({\bf R}$_+)$ . This result is applied to identify a large class of functions for which very general translates enjoy the Riesz basis property in $L_2$({\bf R}$_+)$ .