Functional model for extensions of symmetric operators and applications to scattering theory

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

Research output: Contribution to journalArticle

3 Citations (Scopus)
17 Downloads (Pure)

Abstract

On the basis of the 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, we derive a new representation for the scattering matrix for pairs of such extensions. We use this representation to explicitly recover the coupling constants in the inverse scattering problem for a finite non-compact quantum graph with δ-type vertex conditions.

Original languageEnglish
Pages (from-to)191-215
Number of pages25
JournalNetworks and Heterogeneous Media
Volume13
Issue number2
DOIs
Publication statusPublished - 1 Jun 2018

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Keywords

  • Boundary triples
  • Extensions of symmetric operators
  • Functional model
  • Inverse scattering problems

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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