Scattering theory for a class of non-selfadjoint extensions of symmetric operators

Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov’s spectral form of this model, we find explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices. On the basis of these formulae, we are able to construct wave operators and derive a new representation for the scattering matrix for pairs of such extensions in both self-adjoint and non-self-adjoint situations.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
EditorsP. Kurasov, A. Laptev , S. Naboko, B. Simon
Place of PublicationCham, Switzerland
PublisherSpringer
Pages194-230
Number of pages37
ISBN (Electronic)9783030315313
ISBN (Print)9783030315306
DOIs
Publication statusE-pub ahead of print - 15 Jul 2020

Publication series

NameOperator Theory: Advances and Applications
Volume276
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Boundary triples
  • Extensions of symmetric operators
  • Functional model
  • Scattering theory

ASJC Scopus subject areas

  • Analysis

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