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Riesz Bases in Subspaces of L2 (R+ )

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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 \(L_2$({\bf R}$_+)\) .

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August 5, 1998. Date revised: August 25, 1999. Date accepted: January 11, 2000.

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Goodman, T., Micchelli, C. & Shen, Z. Riesz Bases in Subspaces of L2 (R+ ). Constr. Approx. 17, 39–46 (2001). https://doi.org/10.1007/s003650010019

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  • DOI: https://doi.org/10.1007/s003650010019

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