Strings, dual strings, and related canonical systems

DOI10.1002/mana.200410562zbMath1147.47020OpenAlexW1973677493MaRDI QIDQ5434606

Michael Kaltenbäck, Harald Woracek, Henrik Winkler

Publication date: 7 January 2008

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200410562

zbMATH Keywords

canonical systemFourier transformationstrings with non-homogeneous mass distributionTitchmarsh-Weil coefficient

Mathematics Subject Classification ID

Weyl theory and its generalizations for ordinary differential equations (34B20) General spectral theory of ordinary differential operators (34L05) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Linear operator methods in interpolation, moment and extension problems (47A57) Inverse problems involving ordinary differential equations (34A55)

Related Items (18)

The inverse spectral problem for indefinite strings ⋮ The classical moment problem and generalized indefinite strings ⋮ de Branges Spaces and Growth Aspects ⋮ Two-Dimensional Hamiltonian Systems ⋮ On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations ⋮ A quantitative formula for the imaginary part of a Weyl coefficient ⋮ Szegő condition, scattering, and vibration of Krein strings ⋮ A growth estimate for the monodromy matrix of a canonical system ⋮ Spectral asymptotics for canonical systems ⋮ An inverse spectral theorem for Kreĭn strings with a negative eigenvalue ⋮ Asymptotics of eigenvalues for a class of singular Kreĭn strings ⋮ On a class of integral systems ⋮ A spectral Szegő theorem on the real line ⋮ Canonical systems with discrete spectrum ⋮ Jacobi matrices with lacunary spectrum ⋮ Oscillation theory and semibounded canonical systems ⋮ Estimates for the order of Nevanlinna matrices and a Berezanskii-type theorem ⋮ Order problem for canonical systems and a conjecture of Valent

Cites Work

• Spectral theory of canonical differential systems. Method of operator identities
• Continuation of Hermitian positive definite functions and related questions
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
• On the spectral functions of the string
• Spektralfunktionen einer Klasse von Differentialoperatoren zweiter Ordnung mit nichtlinearem Eigenwertparameter

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