Linearization of boundary eigenvalue problems

DOI10.1007/BF01194929zbMath0736.47017OpenAlexW1982531185WikidataQ124629939 ScholiaQ124629939MaRDI QIDQ1175048

Manfred Möller, Heinz K. Langer

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf01194929

zbMATH Keywords

Banach spacesordinary differential operatorboundary eigenvalue problemslinearizationsoperator colligationsboundary condition depending polynomially on \(\lambda\)boundary conditions depending holomorphically on \(\lambda\)general regular \(\lambda\)-linear first order systeminterval with a \(\lambda\)-depending boundary conditionrealizations of holomorphic operator functionssecond order Sturm-Liouville problem

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items

Sturm--Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions ⋮ Expansion of Analytic Functions in Series of Floquet Solutions of First Order Differential Systems ⋮ Elliptic boundary value problems with \(\lambda \)-dependent boundary conditions ⋮ The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces ⋮ Characteristic Matrices and Spectral Properties of Evolutionary Systems ⋮ A linearization for a class of \(\lambda\)-nonlinear boundary eigenvalue problems

Cites Work

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• Selfadjoint \(\Pi _{\kappa}\)-extensions of symmetric subspaces: An abstract approach to boundary problems with spectral parameter in the boundary conditions
• Analytic equivalence of the boundary eigenvalue operator function and its characteristic matrix function
• Minimal factorization of matrix and operator functions
• Equivalence, linearization, and decomposition of holomorphic operator functions
• Equivalence of boundary eigenvalue operator functions and their characteristic matrix functions
• Self-adjoint subspace extensions satisfying λ-linear boundary conditions
• Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter

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