Multi-interval dissipative Sturm-Liouville boundary-value problems with distributional coefficients

Abstract: The paper investigates spectral properties of multi-interval Sturm-Liouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions in terms of boundary conditions are given. Sufficient conditions for the resolvents of these operators to be operators of the trace class and for the systems of root functions to be complete are found. Results of paper are new for one-interval boundary value problems as well.