Resolvent convergence of Sturm-Liouville operators with singular potentials

Andrii Goriunov; Vladimir Mikhailets

doi:10.1134/S0001434610010372

Resolvent convergence of Sturm-Liouville operators with singular potentials

Functional Analysis 2012-02-21 v1 Mathematical Physics math.MP Spectral Theory

Authors: Andrii Goriunov , Vladimir Mikhailets

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Abstract

In this paper we consider the Sturm-Liuoville operator in the Hilbert space $L_2$ with the singular complex potential of $W^{-1}_2$ and two-point boundary conditions. For this operator we give sufficient conditions for norm resolvent approximation by the operators of the same class.

Keywords

Sturm-Liouville operator singular potential resolvent convergence norm resolvent approximation two-point boundary conditions

Cite

@article{arxiv.1001.4160,
  title  = {Resolvent convergence of Sturm-Liouville operators with singular potentials},
  author = {Andrii Goriunov and Vladimir Mikhailets},
  journal= {arXiv preprint arXiv:1001.4160},
  year   = {2012}
}

Comments

6 pages, to appear in Math. Notes

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