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

2 Citations (Scopus)
13 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

Fingerprint

Symmetric Operator
Functional Model
Scattering Theory
Scattering
Deficiency Index
Quantum Graphs
Closed Operator
Wave Scattering
Scattering Matrix
Inverse Scattering Problem
Unitary group
Explicit Formula
Vertex of a graph
Model

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

Cite this

Functional model for extensions of symmetric operators and applications to scattering theory. / Cherednichenko, Kirill D.; Kiselev, Alexander V.; Silva, Luis O.

In: Networks and Heterogeneous Media, Vol. 13, No. 2, 01.06.2018, p. 191-215.

Research output: Contribution to journalArticle

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