On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator

DOI10.1070/IM8623zbMath1416.34075OpenAlexW2799635905MaRDI QIDQ4568552

Artem M. Savchuk

Publication date: 22 June 2018

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

Full work available at URL: https://doi.org/10.1070/im8623

zbMATH Keywords

Riesz basisDirac operatoreigenfunctionsconditional basisassociated functions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10)

Related Items (6)

Spectral properties of the Dirac operator on the real line ⋮ Estimates of spectral gap lengths for Schrödinger and Dirac operators ⋮ On a variational problem for a model of a Stieltjes string with a backlash at the end ⋮ Unnamed Item ⋮ Stieltjes differential in impulse nonlinear problems ⋮ Spectral properties of classical Dirac operators and operators with involution in homogeneous function spaces

Cites Work

• Characterization of the potential smoothness of one-dimensional Dirac operator subject to general boundary conditions and its Riesz basis property
• Equiconvergence of spectral decompositions for the Dirac system with potential in Lebesgue spaces
• Analog of the Riesz theorem and the basis property in \(L_p\) of a system of root functions of a differential operator. I
• Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions
• Spectral expansions of one-dimensional periodic Dirac operators
• Equivalence in \(L_ p[0,1\) of the system \(e^{i2\pi kx}\) \((k=0,\pm 1,\dots )\) and the system of the eigenfunctions of an ordinary functional-differential operator]
• Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators
• The Dirac operator with complex-valued summable potential
• The L p Behavior of Eigenfunction Expansions
• Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions
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