Sturm-Liouville operators with distributional potentials

Details Sturm-Liouville operators with distributional potentials Sturm-Liouville operators with distributional potentials

2003-01-09

arxiv.org/abs/math/0301077v1

Mathematics

Spectral Theory

Submitted to Proceedings of Moscow Mathematical Society

Scientific paper

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.

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