Skip to main content
Log in

Riesz Bases in Subspaces of L2 (R+ )

  • Published:
Constructive Approximation Aims and scope


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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations


Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goodman, T., Micchelli, C. & Shen, Z. Riesz Bases in Subspaces of L2 (R+ ). Constr. Approx. 17, 39–46 (2001).

Download citation

  • Published:

  • Issue Date:

  • DOI: