Weyl-Titchmarsh \(M\)-functions for \(\varphi\)-periodic Sturm-Liouville operators in terms of Green's functions

DOI10.1007/978-3-031-31139-0_21MaRDI QIDQ6630038

Fritz Gesztesy, Roger Nichols

Publication date: 30 October 2024

zbMATH Keywords

Green's functionsperiodic boundary conditionsWeyl-Titchmarsh theorySturm-Liouville theory

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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• Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials
• Singular Sturm-Liouville Problems: The Friedrichs Extension and Comparison of Eigenvalues
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• Principal Solutions Revisited
• Boundary Value Problems, Weyl Functions, and Differential Operators
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• Floquet theory for partial differential equations
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