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

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

doi:10.3934/nhm.2018009

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

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

Universidad Nacional Autónoma de México
National Pedagogical Dragomanov University

Research output: Contribution to journal › Article › peer-review

15 Citations (SciVal)

104 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 language	English
Pages (from-to)	191-215
Number of pages	25
Journal	Networks and Heterogeneous Media
Volume	13
Issue number	2
DOIs	https://doi.org/10.3934/nhm.2018009
Publication status	Published - 1 Jun 2018

Keywords

Boundary triples
Extensions of symmetric operators
Functional model
Inverse scattering problems

ASJC Scopus subject areas

Statistics and Probability
General Engineering
Computer Science Applications
Applied Mathematics

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10.3934/nhm.2018009

functional_model_extensions_v7.2_NHM
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Networks and Heterogeneous Media, following peer review. The definitive publisher-authenticated versionCherednichenko, K. D., Kiselev, A. V., & Silva, L. O. (2018). Functional model for extensions of symmetric operators and applications to scattering theory. Networks and Heterogeneous Media, 13(2), 191-215, is available online at: https://doi.org/10.3934/nhm.2018009.
Accepted author manuscript, 425 KB

Cite this

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title = "Functional model for extensions of symmetric operators and applications to scattering theory",

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.",

keywords = "Boundary triples, Extensions of symmetric operators, Functional model, Inverse scattering problems",

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year = "2018",

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publisher = "American Institute of Mathematical Sciences",

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AU - Cherednichenko, Kirill D.

AU - Kiselev, Alexander V.

AU - Silva, Luis O.

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Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Boundary triples

KW - Extensions of symmetric operators

KW - Functional model

KW - Inverse scattering problems

UR - https://www.scopus.com/pages/publications/85047057518

U2 - 10.3934/nhm.2018009

DO - 10.3934/nhm.2018009

M3 - Article

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VL - 13

SP - 191

EP - 215

JO - Networks and Heterogeneous Media

JF - Networks and Heterogeneous Media

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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Projects

Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

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