Article
Ufa Mathematical Journal
Volume 9, Number 1, pp. 18-28
Analogue of the Orlov's theorem about deficiency numbers for matrix differential operators of the second order
Braeutigam I.N., Mirzoev K.A., Safonova T.A.
DOI:10.13108/2017-9-1-18
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In this paper we consider the operators generated by the second order matrix linear symmetric quasi-differential expression
l[y]=−(P(y′−Ry))′−R∗P(y′−Ry)+Qy
on the set [1,+∞), where P−1(x), Q(x) are Hermitian matrix functions and R(x) is a complex matrix function of order n with entries pij(x),qij(x),rij(x)∈L1loc[1,+∞) (i,j=1,2,…,n). We describe the minimal closed symmetric operator L0 generated by this expression in the Hilbert space L2n[1,+∞). For this operator we prove an analogue of the Orlov's theorem on the deficiency index of linear scalar differential operators.