Skip to main content
SpringerLink
Log in

Completion by perturbations

  • Published:
Analysis and Mathematical Physics Aims and scope Submit manuscript

Abstract

Any non-complete orthonormal system in a Hilbert space can be transformed into a basis by small perturbations.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bari, N.: Sur les systèmes complets de fonctions orthogonales. Mat. Sbornik 14, 51–108 (1944)

    MathSciNet  MATH  Google Scholar 

  2. Bourgain, J.: A remark on the uncertainty principle for Hilbertian basis. J. Funct. Anal. 79, 136–143 (1988)

    Article  MathSciNet  Google Scholar 

  3. Christensen, O., Deng, B., Heil, C.: Density of Gabor frames. Appl. Comp. Harmon. Anal. 7, 292–304 (1999)

    Article  MathSciNet  Google Scholar 

  4. Olevskii, V.: On orthonormal bases and translates. J. Approx. Theory 202, 1–4 (2016)

  5. Olson, T., Zalik, R.: Nonexistence of a riesz basis of translates. Approx. Theory Lect. Notes Pure Appl. Math 138, 401–408 (1992)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Afeka College of Engineering, Tel Aviv, Israel

    Victor Olevskii

Authors
  1. Victor Olevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Victor Olevskii.

Ethics declarations

Conflict of interest

Author declare that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Olevskii, V. Completion by perturbations. Anal.Math.Phys. 12, 70 (2022). https://doi.org/10.1007/s13324-022-00653-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13324-022-00653-1

Search

Navigation