On Dissipative Dirac Type Operators Containing an Eigenparameter in the Boundary Conditions and with Transmission Conditions

ışıl açık demirci, Bilender Paşaoğlu

Abstract


We consider the dissipative singular Dirac type boundary value transmission problems in the limit circle case, which contain a spectral parameter in the boundary conditions and with transmission conditions. The approach is based on the use of the maximal dissipative operator, and spectral analysis of this operator is sufficient for the boundary value transmission problem. And we construct a self-adjoint dilation of the maximal dissipative operator. We also establish a functional model of the dissipative operator and define its characteristic function in terms of the solutions of the corresponding Dirac type system. Finally, we show that all eigenvectors and associated vectors are complete in the space L_{X}²(Θ;ℂ²).

Keywords


Dissipative operator; Transmission condition; Eigenvalue problem; Dissipative singular Dirac system; Maximal dissipative operator; Functional model; Characteristic function; Completeness of the system of eigenvectors and associated vectors.

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