Sergey Naboko's legacy on the spectral theory of Jacobi operators

DOI10.1007/978-3-031-31139-0_5MaRDI QIDQ6630022

Luis O. Silva, Sergey Simonov

Publication date: 30 October 2024

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Schrödinger operator, Schrödinger equation (35J10) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Meromorphic functions of one complex variable (general theory) (30D30) Canonical models for contractions and nonselfadjoint linear operators (47A45) Linear operators on spaces with an indefinite metric (47B50) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Elliptic operators and their generalizations (47F10) Nonselfadjoint operators (47B28)

Cites Work

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• On the inverse resonance problem for Jacobi operators -- uniqueness and stability
• Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach
• Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: Elementary methods
• Unbounded Jacobi matrices with a few gaps in the essential spectrum: Constructive examples
• The inverse resonance problem for Hermite operators
• Unbounded Jacobi matrices at critical coupling
• Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis
• Asymptotic behavior of generalized eigenvectors of Jacobi matrices in the critical (``double root) case
• Dense point spectra of Schrödinger and Dirac operators
• Jacobi matrices with power-like weights -- grouping in blocks approach
• On the point spectrum of discrete Schrödinger operator
• On new relations between spectral properties of Jacobi matrices and their coefficients
• Eigenvalue asymptotics of a modified Jaynes--Cummings model with periodic modulations.
• Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries
• On the instability of the essential spectrum for block Jacobi matrices
• The essential spectrum of some unbounded Jacobi matrices: a generalization of the Last-Simon approach
• Green matrix estimates of block Jacobi matrices. I: Unbounded gap in the essential spectrum
• Green matrix estimates of block Jacobi matrices. II: Bounded gap in the essential spectrum
• Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case
• On the point spectrum of periodic Jacobi matrices with matrix entries: elementary approach
• Zeroes of the spectral density of the periodic Schrödinger operator with Wigner-von Neumann potential
• Elementary models of unbounded Jacobi matrices with a few bounded gaps in the essential spectrum
• Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
• Decay Bounds on Eigenfunctions and the Singular Spectrum of Unbounded Jacobi Matrices
• Jacobi matrices with absolutely continuous spectrum
• Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique
• Infinite Jacobi Matrices with Unbounded Entries: Asymptotics of Eigenvalues and the Transformation Operator Approach
• Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach
• ESTIMATES OF GENERALIZED EIGENVECTORS OF HERMITIAN JACOBI MATRICES WITH A GAP IN THE ESSENTIAL SPECTRUM
• The Inverse Resonance Problem for Jacobi Operators

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