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A completeness theorem for a dissipative Schrödinger problem with the spectral parameter in the boundary condition

✍ Scribed by M. Yakít Ongun; Bilender P. Allahverdiev

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
188 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper we consider a dissipative Schrödinger boundary value problem in the limit‐circle case with the spectral parameter in the boundary condition. The approach is based on the use of the maximal dissipative operator, and the spectral analyzes of this operator is adequate for the boundary value problem to be solved. We construct a self‐adjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrödinger equation. We prove theorems on the completeness of the system of eigenvectors and associated vectors of the maximal dissipative operator and the Schrödinger boundary value problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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