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Limit-point criteria for the matrix Sturm-Liouville operator and its powers

Braeutigam I. N.

Opuscula Mathematica

2017

Vol. 37, no. 1

5--19

We consider matrix Sturm-Liouville operators generated by the formal expression [formula] in the space [formula]. Let the matrix functions P := P(x), Q := Q(x) and R := R(x) of order n (n ∈ N) be defined on I, P is a nondegenerate matrix, P and Q are Hermitian matrices for x ∈ I and the entries of the matrix functions[formula], 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 [formula]. In particular, we obtain limit-point conditions for Sturm-Liouville operators with matrix-valued distributional coefficients.