Dissipative Sturm-Liouville operators with nonseparated boundary conditions (Q1411605)

The minimal symmetric singular Sturm-Liouville operator \[ \ell y:=(w(x))^{-1}(-(p(x)y'(x))'+q(x)y(x)) \] is studied in the Hilbert space \(L^2_w(a,b)\), \(-\infty\leq a<b\leq\infty\) with defect index (2,2). A space of boundary values is constructed and all maximal dissipative and selfadjoint extensions are described in terms of the boundary conditions. A theorem on the completeness of the system of eigenfunctions and associated functions of dissipative Sturm-Liouville operators is proved. [This paper also appeared in Rocky Mt. J. Math. 35, 367-390 (2005).]