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

DOI10.3934/nhm.2018009OpenAlexW3101059048WikidataQ129821540 ScholiaQ129821540MaRDI QIDQ1713380

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

Publication date: 24 January 2019

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.06220

zbMATH Keywords

functional modelinverse scattering problemsboundary triplesextensions of symmetric operators

Mathematics Subject Classification ID

Canonical models for contractions and nonselfadjoint linear operators (47A45) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items

Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions, Spectral enclosures for non-self-adjoint extensions of symmetric operators, Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I, FUNCTIONAL MODEL FOR BOUNDARY‐VALUE PROBLEMS, The functional model for maximal dissipative operators (translation form): An approach in the spirit of operator knots, Scattering theory for a class of non-selfadjoint extensions of symmetric operators, Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems, Time-Dispersive Behavior as a Feature of Critical-Contrast Media, Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media, On the S-matrix of Schrödinger operator with nonlocal δ-interaction

Cites Work

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• Isospectrality for graph Laplacians under the change of coupling at graph vertices
• Perturbation of the continuous spectrum and unitary equivalence
• Null-range potentials and M. G. Krejn's formula for generalized resolvents
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Extensions of symmetric operators and symmetric binary relations
• Über adjungierte Funktionaloperatoren
• Theory of self-adjoint extensions of symmetric operators. Entire operators and boundary-value problems
• Scattering theory for open quantum systems with finite rank coupling
• The abstract theory of scattering
• Harmonic analysis of operators on Hilbert space
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions
• On inverse topology problem for Laplace operators on graphs
• Scattering theory for the matrix Schrödinger operator on the half line with general boundary conditions
• ISOSPECTRALITY FOR GRAPH LAPLACIANS UNDER THE CHANGE OF COUPLING AT GRAPH VERTICES: NECESSARY AND SUFFICIENT CONDITIONS
• Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• Inverse problems for Aharonov–Bohm rings
• Functional Model of a Class of Non-selfadjoint Extensions of Symmetric Operators
• Dilation theory and spectral analysis of nonselfadjoint differential operators
• The Inverse Problem in the Quantum Theory of Scattering
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
• ON SEPARATION CONDITIONS FOR THE SPECTRAL COMPONENTS OF A DISSIPATIVE OPERATOR
• Inverse scattering on the line
• Kirchhoff's rule for quantum wires
• A duality between Schroedinger operators on graphs and certain Jacobi matrices
• Scattering theory for a class of non-selfadjoint extensions of symmetric operators
• Conditions for the Existence of the Generalized Wave Operators
• On unitary couplings of semiunitary operators
• On the perturbation of continuous spectra