Riesz Bases in Subspaces of L2 (R+ )

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 arose. In this paper, we provide a sufficient condition to determine whether the nonnegative translates form a Riesz system on . This result is applied to identify a large class of functions for which very general translates enjoy the Riesz basis property in . August 5, 1998. Date revised: August 25, 1999. Date accepted: January 11, 2000.