Regularization of singular Sturm-Liouville equations

Details Regularization of singular Sturm-Liouville equations Regularization of singular Sturm-Liouville equations

2010-02-23

arxiv.org/abs/1002.4371v2

Methods Funct. Anal. Topology 16 (2010), no. 2, 120-130

Mathematics

Functional Analysis

12 pages

Scientific paper

Paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ on a finite interval with coefficients $$q = Q', \quad 1/p, Q/p, Q^2/p \in L_1,$$ where derivative of the function $Q$ is understood in the sense of distributions. Due to a new regularization corresponding operators are correctly defined as quasi-differential. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonic form. Some results are new for the case $p(t)\equiv 1$ as well.

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