Sturm-Liouville operators with distributional potentials

By A. Savchuk, A. Shkalikov. 2003

242 citations recorded by the source corpus.

In this paper we propose four different methods to determine Sturm-Liouville operator on an interval $(a,b)$ in case, when a potential $q(x)$ is a distribution from the Sobolev space with negative index of smoothness, i.e. (q\in W_2^{-\theta}), where (\theta\le 1). The main and second terms of asymptotic series for eigenvalues and eigenfunctions of these operators are obtained and the remaining terms are estimated depending on the class of smoothness of potential /(q/). Particular families of potentials, not belonging to the space (W_2^{-1}) are studied as well.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe98ddb709e91aaad194df1d50e4f2f6f02c5c41

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In Applied Mathematics

1. Y. Mykytyuk
2. Rostyslav Hryniv
3. Peter Perry
4. P. Topalov
5. Thomas Kappeler
6. S. Benenti

In Mathematical Physics

1. Y. Mykytyuk
2. Rostyslav Hryniv
3. P. Topalov
4. Thomas Kappeler

Citations in the corpus

• The Miura map on the line (2005, background): “See also [20], [21], [23], [29], [30], [37], [40], [41] as well as [41] for further references.”
• Transformation Operators for Sturm-Liouville Operators with Singular Potentials (2004, methodology): “Savchuk and A.A.Shkalikov,Sturm {Liouvilleoperatorswith singularpotentials,M atem .”