An analog of Orlov’s theorem on the deficiency index of second-order differential operators

Braeutigam, I. N.; Mirzoev, K. A.; Safonova, T. A.

doi:10.1134/s0001434615010332

Cited by 2 publications

(2 citation statements)

References 2 publications

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“…. , 2k) of a given vector function y ∈ AC n,loc (I) assuming [1] := P (y − Ry), y [2] := (y [1] ) + R * y [1] − Qy, y [3] := P ((y [2] ) − Ry [2] ), y [4] := (y [3] ) + R * y [3] − Qy [2] , . .…”

Section: 2mentioning

confidence: 99%

“…In [13] the authors obtained several criteria for a matrix Sturm-Liouville-type equation of special form to have maximal deficiency indices. In [3] it is presented the conditions on the coefficients of the expression (1.2) such that the deficiency numbers of the operator L 0 are defined as the number of roots of a special kind polynomial lying in the left half-plane. The authors of [11] established a relationship between the spectral properties of the matrix Schrödinger operator with point interactions on the half-axis and block Jacobi matrices of certain class.…”

Section: 3mentioning

confidence: 99%

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

Braeutigam¹

2017

OpMath

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Abstract. We consider matrix Sturm-Liouville operators generated by the formal expression ). 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 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 ∈ N). In particular, we obtain limit-point conditions for Sturm-Liouville operators with matrix-valued distributional coefficients.

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