ASYMPTOTICS OF EIGENVALUES AND EIGENFUNCTIONS OF THE STURM–LIOUVILLE OPERATOR WITH SINGULAR POTENTIAL ON A STAR GRAPH. I

Spectral problems on a star-graph consisting of three edges with a Sturm–Liouville operator defined on each of them are investigated. The spectral properties of such operators have been studied, in particular, asymptotic formulas for eigenvalues and eigenfunctions of the operator with Dirichlet boundary conditions at free ends and continuity and Kirchhoff conditions at a common vertex have been obtained. The potential in the Sturm–Liouville problem is assumed to be singular, it is a derivative of a quadratically summable function in sense of distributions.