limit-point criteria for the matrix sturm-liouville operator and its powers

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ID: 142965
2017
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Abstract
We consider matrix Sturm-Liouville operators generated by the formal expression \[l[y]=-(P(y^{\prime}-Ry))^{\prime}-R^*P(y^{\prime}-Ry)+Qy,\] in the space \(L^2_n(I)\), \(I:=[0, \infty)\). Let the matrix functions \(P:=P(x)\), \(Q:=Q(x)\) and \(R:=R(x)\) of order \(n\) (\(n \in \mathbb{N}\)) be defined on \(I\), \(P\) is a nondegenerate matrix, \(P\) and \(Q\) are Hermitian matrices for \(x \in I\) and the entries of the matrix functions \(P^{-1}\), \(Q\) and \(R\) are measurable on \(I\) and integrable on each of its closed finite subintervals. The main purpose of this paper is to find conditions on the matrices \(P\), \(Q\) and \(R\) that ensure the realization of the limit-point case for the minimal closed symmetric operator generated by \(l^k[y]\) (\(k \in \mathbb{N}\)). In particular, we obtain limit-point conditions for Sturm-Liouville operators with matrix-valued distributional coefficients.
Reference Key
braeutigam2017opusculalimit-point Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Irina N. Braeutigam
Journal zhonghua yi xue za zhi
Year 2017
DOI
http://dx.doi.org/10.7494/OpMath.2017.37.1.5
URL
http://www.opuscula.agh.edu.pl/vol37/1/art/opuscula_math_3701.pdf
Keywords
quantitative methods

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