On the completeness and Riesz basis property of root subspaces of boundary value problems for first order systems and applications

DOI10.4171/JST/90zbMath1333.47038arXiv1401.2574MaRDI QIDQ2347238

Anton A. Lunyov, Mark M. Malamud

Publication date: 27 May 2015

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.2574

zbMATH Keywords

completeness of root vectorsRiesz basis propertyregular boundary conditionssystems of ordinary differential equationsTimoshenko beam model

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Initial-boundary value problems for higher-order hyperbolic equations (35L35)

Related Items (17)

On the Riesz basis property of root vectors system for \(2\times 2\) Dirac type operators ⋮ On nonlocal perturbation of the problem on eigenvalues of differentiation operator on a segment ⋮ Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators ⋮ On the exponential stability of Beck's problem on a star-shaped graph ⋮ Criterion of Bari basis property for 2 × 2 Dirac‐type operators with strictly regular boundary conditions ⋮ On convergence of spectral expansions of Dirac operators with regular boundary conditions ⋮ Dependence of eigenvalues of Dirac system on the parameters ⋮ Spectral analysis of a non‐homogeneous rotating Timoshenko beam ⋮ On the properties of the root vector function systems of a \(2m\)th-order Dirac type operator with an integrable potential ⋮ Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients ⋮ On the completeness of eigenfunctions of a discontinuous Dirac operator with an eigenparameter in the boundary condition ⋮ Asymptotic behavior of solutions of the Dirac system with an integrable potential ⋮ Dirac-Krein systems on star graphs ⋮ Spectral theory of rank one perturbations of normal compact operators ⋮ Stability of spectral characteristics of boundary value problems for \(2 \times 2\) Dirac type systems: applications to the damped string ⋮ Completeness property of one-dimensional perturbations of normal and spectral operators generated by first order systems ⋮ Inverse problem for the Schrödinger equation with non-self-adjoint matrix potential

Cites Work

• Bari–Markus property for Riesz projections of 1D periodic Dirac operators
• Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions
• The method of similar operators in the spectral analysis of non-self-adjoint Dirac operators with non-smooth potentials
• Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials
• Unnamed Item

This page was built for publication: On the completeness and Riesz basis property of root subspaces of boundary value problems for first order systems and applications