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 $l[y]=-(y^{\prime}-Py) ^{\prime}-P(y^{\prime}-Py)-P^2y$, where $^{\prime}$ is a derivative in sense of the theory of distributions and $P$ is a real-valued symmetrical matrix with elements $p_{ij}\in L^2_{loc}(R_+)$ ($i,j=1,2,\ldots,n$). The minimal closed symmetric operator $L_0$ generated in Hilbert space $\mathcal{L}^2_n(R_+)$ this expression are constructed. Sufficient condi-\\tions of a minimality and maximality of deficiency numbers of the operator $L_0 $ 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 $L_0 $ (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 $l^2_n $.