Article
Ufa Mathematical Journal
Volume 3, Number 3, pp. 102-115
Singular Sturm-Liouville operators with nonsmooth potentials in space of vector functions
Mirzoev K.A., Safonova T.A.
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This paper deals with Sturm-Liouville operators generated on the semi-axis by the differential expression l[y]=−(y′−Py)′−P(y′−Py)−P2y, where ′ is a derivative in sense of the theory of distributions and P is a real-valued symmetrical matrix with elements pij∈L2loc(R+) (i,j=1,2,…,n). The minimal closed symmetric operator L0 generated in Hilbert space L2n(R+) this expression are constructed. Sufficient condi-\\tions of a minimality and maximality of deficiency numbers of the operator L0 in terms of elements of a matrix P are resulted. In addition it is established, that a condition of maximality of deficiency numbers of the operator L0 (in a case when elements of a matrix P are step functions with infinite number of jumps) equivalence to a condition of maximality of deficiency numbers of the operator generated some generalized Jacobi matrices in space l2n.