Spectral analysis of nonselfadjoint Schrodinger problem with eigenparameter in the boundary condition

Ongun M. Y.

SCIENCE IN CHINA SERIES A-MATHEMATICS, vol.50, no.2, pp.217-230, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1007/s11425-007-0006-7
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.217-230
  • Süleyman Demirel University Affiliated: No


In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint 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 construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.