Abstract.
A space of boundary values is constructed for the minimal symmetric singular Sturm-Liouville operator in the Hilbert space \(L_{w}^{2}(a,b)(-\infty \le a < b \le \infty )\) with defect index (2,2) (in Weyl’s limit-circle cases at singular points a and b). A description of all maximal dissipative, maximal accretive, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions at a and b. We investigate maximal dissipative operators with, generally speaking, nonseparated boundary conditions. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We also construct a functional model of a dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.
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Received February 18, 2002; in revised form January 31, 2003 Published online July 15, 2003
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Allahverdiev, B. Dissipative Sturm-Liouville Operators with Nonseparated Boundary Conditions. Monatsh. Math. 140, 1–17 (2003). https://doi.org/10.1007/s00605-003-0035-4
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DOI: https://doi.org/10.1007/s00605-003-0035-4