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

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

doi:10.1007/978-3-030-31531-3_14

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 proceeding › Chapter

1 Citation (SciVal)

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 language	English
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Editors	P. Kurasov, A. Laptev , S. Naboko, B. Simon
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	194-230
Number of pages	37
ISBN (Electronic)	9783030315313
ISBN (Print)	9783030315306
DOIs	https://doi.org/10.1007/978-3-030-31531-3_14
Publication status	E-pub ahead of print - 15 Jul 2020

Publication series

Name	Operator Theory: Advances and Applications
Volume	276
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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10.1007/978-3-030-31531-3_14

Cite this

Cherednichenko, K. D., Kiselev, A. V., & Silva, L. O. (2020). Scattering theory for a class of non-selfadjoint extensions of symmetric operators. In P. Kurasov, A. Laptev , S. Naboko, & B. Simon (Eds.), Operator Theory: Advances and Applications (pp. 194-230). (Operator Theory: Advances and Applications; Vol. 276). Springer. https://doi.org/10.1007/978-3-030-31531-3_14

Scattering theory for a class of non-selfadjoint extensions of symmetric operators. / Cherednichenko, Kirill D.; Kiselev, Alexander V.; Silva, Luis O.

Operator Theory: Advances and Applications. ed. / P. Kurasov; A. Laptev ; S. Naboko; B. Simon. Cham, Switzerland : Springer, 2020. p. 194-230 (Operator Theory: Advances and Applications; Vol. 276).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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N2 - 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.

AB - 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.

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KW - Scattering theory

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T3 - Operator Theory: Advances and Applications

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A2 - Laptev , A.

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A2 - Simon, B.

PB - Springer

CY - Cham, Switzerland

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

Abstract

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

Abstract

Publication series

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

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

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this