The Riesz basis property of generalized eigenspaces for a Dirac system with integrable potential

DOI10.1134/S1064562415030163zbMath1478.34097OpenAlexW2273002272MaRDI QIDQ498196

I. V. Sadovnichaya, Artem M. Savchuk

Publication date: 28 September 2015

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

Full work available at URL: https://doi.org/10.1134/s1064562415030163

zbMATH Keywords

completenessminimalityeigenfunctions and associated functionsone-dimensional Dirac operatorRiesz basis properties

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10)

Related Items (11)

Dirac system with potential lying in Besov spaces ⋮ Equiconvergence of spectral decompositions for the Dirac system with potential in Lebesgue spaces ⋮ Bessel inequality and the basis property for a \(2m\times 2m\) Dirac type system with an integrable potential ⋮ On the stability of the solution of the inverse problem for Dirac operator ⋮ Criterion of Bari basis property for 2 × 2 Dirac‐type operators with strictly regular boundary conditions ⋮ Asymptotic behavior of solutions of the Dirac system with an integrable potential ⋮ Estimates of Riesz constants for the Dirac system with an integrable potential ⋮ Uniform asymptotics of the eigenvalues and eigenfunctions of the Dirac system with an integrable potential ⋮ Some properties of functional-differential operators with involution \(\nu(x)=1-x\) and their applications ⋮ 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

Cites Work

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• Asymptotic formulas for fundamental solutions of the Dirac system with complex-valued integrable potential
• On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations
• On the Riesz basis property of the root vector system for Dirac-type \(2\times 2\) systems
• Bari–Markus property for Riesz projections of 1D periodic Dirac operators
• Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

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