On the Riesz basis property of the root vector system for Dirac-type \(2\times 2\) systems

DOI10.1134/S106456241406012XzbMath1323.34094MaRDI QIDQ2254105

Anton A. Lunyov, Mark M. Malamud

Publication date: 4 February 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

eigenfunctionsorthogonalityDirac systemsRiesz basis propertycompletenees

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10)

Related Items (13)

On the Riesz basis property of root vectors system for \(2\times 2\) Dirac type operators ⋮ Bessel inequality and the basis property for a \(2m\times 2m\) Dirac type system with an integrable potential ⋮ Criterion of Bari basis property for 2 × 2 Dirac‐type operators with strictly regular boundary conditions ⋮ On spectral synthesis for dissipative Dirac type operators ⋮ On convergence of spectral expansions of Dirac operators with regular boundary conditions ⋮ The Riesz basis property of generalized eigenspaces for a Dirac system with integrable potential ⋮ Regular boundary value problems for the Dirac operator ⋮ Asymptotic behavior of solutions of the Dirac system with an integrable potential ⋮ Dirac-Krein systems on star graphs ⋮ Bessel property and basicity of the system of root vector-functions of Dirac operator with summable coefficient ⋮ 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 ⋮ The Dirac operator with complex-valued summable potential

Cites Work

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• On spectral synthesis for dissipative Dirac type operators
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• On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations
• Theorem of completeness for a Dirac-type operator with generalized \(\lambda \)-depending boundary conditions
• Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators
• Bari–Markus property for Riesz projections of 1D periodic Dirac operators
• Spectral properties and an inverse eigenvalue problem for non-symmetric systems of ordinary differential 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

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