Skip to main content
SpringerLink
Log in

Equiconvergence theorems for singular Sturm-Liouville operators with various boundary conditions

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider the Sturm-Liouville operator L(y) = −d 2 y/dx 2 + q(x)y in the space L 2[0, π], where the potential q(x) is a complex-valued distribution of the first order of singularity; namely, q(x) = ut’(x), where u ∈ L 2[0, π]. (The derivative is understood in the sense of distributions.) We study the uniform equiconvergence on the entire interval [0, π] of the expansions of a function f ∈ L 2 in the system of eigenfunctions and associated functions of the operator L with the Fourier trigonometric series expansion. We also estimate the equiconvergence rate.

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. Savchuk, A.M. and Shkalikov, A.A., Sturm-Liouville Operators with Singular Potentials, Mat. Zametki, 1999, vol. 66, no. 6, pp. 897–912.

    Article  MathSciNet  Google Scholar 

  2. Savchuk, A.M. and Shkalikov, A.A., Sturm-Liouville Operators with Distribution Potentials, Tr. Mosk. Mat. Obs., 2003, vol. 64, pp. 159–219.

    MathSciNet  Google Scholar 

  3. Savchuk, A.M., On Eigenfunctions of the Sturm-Liouville Operator with Potentials from Sobolev Spaces, arXiv, 2010, no. 1003.3172.

    Google Scholar 

  4. Sadovnichaya, I.V., Equiconvergence of Expansions in Series in Eigenfunctions of Sturm-Liouville Operators with Distribution Potentials, Mat. Sb., 2010, vol. 201, no. 9, pp. 61–76.

    Article  MathSciNet  Google Scholar 

  5. Sadovnichaya, I.V., On the Rate of Equiconvergence of Expansions in Series in a Trigonometric System and in Eigenfunctions of the Sturm-Liouville Operator with Distribution Potential, Differ. Uravn., 2008, vol. 44, no. 5, pp. 656–664.

    MathSciNet  Google Scholar 

  6. Shveikina, O.A., On the Asymptotics of Eigenfunctions of Sturm-Liuoville Operators with Distribution Potentials, Differ. Uravn., 2013, vol. 49, no. 8, pp. 985–992.

    MathSciNet  Google Scholar 

  7. Shveikina, O.A., Theorems on Asymptotics of Sturm-Liouville Singular Operators with Various Boundary Conditions, Differ. Uravn., 2014, vol. 50, no. 5, pp. 626–635.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    O. A. Shveikina

Authors
  1. O. A. Shveikina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. A. Shveikina.

Additional information

Original Russian Text © O.A. Shveikina, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 174–182.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shveikina, O.A. Equiconvergence theorems for singular Sturm-Liouville operators with various boundary conditions. Diff Equat 51, 177–185 (2015). https://doi.org/10.1134/S0012266115020032

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266115020032

Keywords

Search

Navigation