Regularization of singular Sturm-Liouville equations

2010/02/28 by Andrii Goriunov, Vladimir Mikhailets · 1 citation
Mathematics · Physics and Astronomy · #math.FA #math-ph #math.MP #math.SP #msc:34L40 #msc:34B08 #msc:47A10

paper · pdf

published as Methods Funct. Anal. Topology 16 (2010), no. 2, 120-130 · 12 pages

arxiv created 2010/07/08 · arxiv updated 2010/08/17

Abstract

Paper deals with the singular Sturm-Liouville expressions l(y) = -(py')' + qy on a finite interval with coefficients q = Q', 1/p, Q/p, Q²/p ∈ L₁, 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)≡ 1 as well.

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• Sturm-Liouville operators with matrix distributional coefficients

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