Asymptotics of Eigenvalues and Eigenfunctionsof the Sturm–Liouville Operator with a Singular Potential on a Star Graph: II

Spectral problems on a star graph consisting of three edges with a Sturm–Liouville operator defined on each of them are studied. We analyze the spectral properties of such operators; in particular, we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the operator with the Dirichlet boundary conditions at the free ends and the continuity and Kirchhoff conditions at the common vertex. The potential in the Sturm–Liouville problem is assumed to be singular; namely, it is the distributional derivative of a square integrable function.