Sturm-Liouville systems with rational Weyl functions: Explicit formulas and applications

DOI10.1007/BF01195588zbMath0897.34025MaRDI QIDQ1384116

Israel Gohberg, Alexander L. Sakhnovich, Marinus A. Kaashoek

Publication date: 19 October 1998

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Sturm-Liouville systemsdirect and inverse spectral problemsrational Weyl functions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) KdV equations (Korteweg-de Vries equations) (35Q53) Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) General systems theory (93A99)

Related Items (7)

Explicit solutions of matrix and dynamical Schrödinger equations and of KdV equation in terms of square roots of the generalised matrix eigenvalues ⋮ Inverse problem for Sturm-Liouville operators with rational reflection coefficient ⋮ Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications ⋮ Commutation methods for Schrödinger operators with strongly singular potentials ⋮ Dressing for Fokker-Planck Equations: the Cases of 1+1 and 1+ℓ Dimensions ⋮ Continuous and discrete dynamical Schrödinger systems: explicit solutions ⋮ Generalized Bäcklund-Darboux transformation: Spectral properties and nonlinear equations

Cites Work

• Differential equations in the spectral parameter
• Iterated Bäcklund-Darboux transform for canonical systems
• Iterated Bäcklund-Darboux transformation and transfer matrix-function (nonisospectral case).
• Rational solutions of nonlinear evolution equations, vertex operators, and bispectrality
• Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications
• Inverse spectral problems for difference operators with rational scattering matrix function
• Inverse spectral problem for differential operators with rational scattering matrix functions
• Canonical Systems with Rational Spectral Densities: Explicit Formulas and Applications
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