WIAS Preprint No. 664, (2001)

On one dimensional dissipative Schrödinger-type operators, their dilations and eigenfunction expansions



Authors

  • Kaiser, Hans-Christoph
  • Neidhardt, Hagen
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 47B44 47E05

Keywords

  • dissipative Schrödinger-type operators, Sturm-Liouville operators, characteristic function, minimal dilation, eigenfunction expansion

Abstract

We study in detail Schrödinger-type operators on a bounded interval of the real axis with dissipative boundary conditions. The characteristic function of such operators is computed, its minimal self-adjoint dilation is constructed and the generalized eigenfunction expansion for the dilation is developed. The problem is motivated by semiconductor physics.

Appeared in

  • Mathematische Nachrichten, 2003, Vol. 252, pp.51-69

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