Linear operator pencils \(A-\lambda B\) with discrete spectrum

DOI10.1007/BF01194485zbMath0977.47012MaRDI QIDQ1583713

Christiane Tretter

Publication date: 17 January 2002

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

zbMATH Keywords

eigenvectorscompletenessminimalityspectral properties of pencils

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) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (17)

Spectral theory for perturbed Krein Laplacians in nonsmooth domains ⋮ Remarks on the application of the Keldysh theorem on the completeness of root subspace of non-self-adjoint operators and comments on ``Spectral operators generated by Timoshenko beam model ⋮ On the completeness of root vectors generated by systems of coupled hyperbolic equations ⋮ Eigenvalue problem of a class of fourth-order Hamiltonian operators ⋮ The quasi-Weierstrass form for regular matrix pencils ⋮ Linear pencils and quadratic programming problems with a quadratic constraint ⋮ On spectral properties of dissipative fourth order boundary-value problem with a spectral parameter in the boundary condition ⋮ On the completeness of root vectors of a certain class of differential operators ⋮ One-dimensional approximations of the eigenvalue problem of curved rods ⋮ Boundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditions ⋮ On completeness of spectral subspaces of linear relations and ordered pairs of linear operators ⋮ Boundary pairs associated with quadratic forms ⋮ Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators ⋮ A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains ⋮ A linearization for a class of \(\lambda\)-nonlinear boundary eigenvalue problems ⋮ Generalized eigenvectors of linear operators and biorthogonal systems ⋮ Riesz Bases of Port-Hamiltonian Systems

Cites Work

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• Elliptic equations in Hilbert space and associated spectral problems
• Boundary problems for ordinary differential equations with parameter in the boundary conditions
• Nonselfadjoint spectral problems for linear pencils \(N- \lambda P\) of ordinary differential operators with \(\lambda\)-linear boundary conditions: Completeness results
• Kamke Problems. Properties of the Eigenfunctions
• Spectral Analysis for Linear Pencils N — λP of Ordinary Differential Operators

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