Riesz bases in subspaces of L-2(R+)

In a recent investigation [8] concerning the asymptotic behavior of Gram-Sc hmidt orthonormalization procedure applied to the nonnegative integer shift s of a given function, the problem of determining whether or not such funct ions form a Riesz system in L-2(R+) arose. In this paper, we provide a suff icient condition to determine whether the nonnegative translates form a Rie sz system on L-2(R+). This result is applied to identify a large class of f unctions for which very general translates enjoy the Riesz basis property i n L-2(R+).