Dissipative eigenvalue problems for a Sturm-Liouville operator with a singular potential

In this paper we consider the Sturm-Liouville operator d(2)/dx(2) - 1/x on the interval [a, b], a < 0 < b, with Dirichlet boundary conditions at a and b, for which x = 0 is a singular point. In the two components L-2(a, 0) an d L-2(0, b) of the space L-2 (a, b) = L-2(a, 0) + L-2(0, b) we define minim al symmetric operators and describe all the maximal dissipative and self-ad joint extensions of their orthogonal sum in L-2 (a, b) by interface conditi ons at x = 0. We prove that the maximal dissipative extensions whose domain contains only continuous functions f are characterized by the interface co ndition lim(x-->0+)(f'(x) - f'(-x)) = gammaf(0) with gamma is an element of C+ boolean OR R or by the Dirichlet condition f(0+) = f(0-) = 0. We also s how that the corresponding operators can be obtained by norm resolvent appr oximation from operators where the potential 1/x is replaced by a continuou s function, and that their eigen and associated functions can be chosen to form a Bari basis in L-2(a, b).