Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions
From MaRDI portal
Publication:4918594
DOI10.1512/iumj.2012.61.4531zbMath1297.47047arXiv1008.4095OpenAlexW2061855360MaRDI QIDQ4918594
Boris S. Mityagin, Plamen Djakov
Publication date: 25 April 2013
Published in: Indiana University Mathematics Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1008.4095
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
On stability of basis property of root vectors system of the Sturm-Liouville operator with an integral perturbation of conditions in nonstrongly regular Samarskii-Ionkin type problems ⋮ On the Riesz basis property of root vectors system for \(2\times 2\) Dirac type operators ⋮ \(L_\mu\to L_\nu\) equiconvergence of spectral decompositions for a Dirac system with \(L_\kappa\) potential ⋮ Uniform basis property of root vector systems of Dirac operators ⋮ 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 ⋮ On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator ⋮ Spectral properties of the Dirac operator on the real line ⋮ On the asymptotic behaviour of solutions of the Dirac system and applications to the Sturm-Liouville problem with a singular potential ⋮ 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 the completeness of systems of root vectors for first-order systems: application to the Regge problem ⋮ On spectral synthesis for dissipative Dirac type operators ⋮ On convergence of spectral expansions of Dirac operators with regular boundary conditions ⋮ On periodic and antiperiodic spectra of non-self-adjoint Dirac operators ⋮ On the properties of the root vector function systems of a \(2m\)th-order Dirac type operator with an integrable potential ⋮ On the spectrum of non-self-adjoint Dirac operators with quasi-periodic boundary conditions ⋮ Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions ⋮ The Riesz basis property of generalized eigenspaces for a Dirac system with integrable potential ⋮ On the completeness of eigenfunctions of a discontinuous Dirac operator with an eigenparameter in the boundary condition ⋮ Regular boundary value problems for the Dirac operator ⋮ Asymptotic behavior of solutions of the Dirac system with an integrable potential ⋮ The Riesz basis property with brackets for Dirac systems with summable potentials ⋮ On the Riesz basis property of the root vector system for Dirac-type \(2\times 2\) systems ⋮ Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators ⋮ On the Riesz inequality and the basis property of systems of root vector functions of a discontinuous Dirac operator ⋮ Spectral properties of the Dirac operator with a nonsmooth potential of the general form and operator groups ⋮ On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations ⋮ Estimates of Riesz constants for the Dirac system with an integrable potential ⋮ Equiconvergence of spectral decompositions for Sturm-Liouville operators: triples of Lebesgue spaces ⋮ On the existence of an operator group generated by the one-dimensional Dirac system ⋮ Spectral asymptotics of solutions of a \(2\times 2\) system of first-order ordinary differential equations ⋮ Bessel property and basicity of the system of root vector-functions of Dirac operator with summable coefficient ⋮ Classical equiconvergence problem for the Sturm-Liouville operator with a singular potential ⋮ 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 ⋮ On the completeness and Riesz basis property of root subspaces of boundary value problems for first order systems and applications
