Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions

By B. Allahverdiev, E. Bairamov, Ekin Uğurlu. 2013

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Abstract In this paper, we investigate the nonselfadjoint (dissipative) boundary value transmission problems in Weyl’s limit-circle case. At first using the method of operator-theoretic formulation we pass to a new operator. After showing that this new operator is a maximal dissipative operator, we construct a selfadjoint dilation of the maximal dissipative operator. Using the equivalence of the Lax–Phillips scattering function and the Sz.-Nagy-Foias characteristic function, we show that all eigenfunctions and associated functions are complete in the space L w 2 ( Ω ) .

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/da19a99127a781dcc90a689e795707b2fd80df06