Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

DOI10.1016/j.jat.2012.03.013zbMath1258.34174arXiv1108.0344OpenAlexW1975683133MaRDI QIDQ435171

Plamen Djakov, Boris S. Mityagin

Publication date: 11 July 2012

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

Full work available at URL: https://arxiv.org/abs/1108.0344

zbMATH Keywords

equiconvergenceDirac operatorRiesz basesspectral decompositions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenvalue problems for linear operators (47A75) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Approximation by other special function classes (41A30)

Related Items (15)

On the Riesz basis property of root vectors system for \(2\times 2\) Dirac type operators ⋮ On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator ⋮ Asymptotic formulas for fundamental solutions of the Dirac system with complex-valued integrable potential ⋮ On spectral synthesis for dissipative Dirac type operators ⋮ On convergence of spectral expansions of Dirac operators with regular boundary conditions ⋮ Perturbations of self-adjoint and normal operators with discrete spectrum ⋮ ON THE SPECTRAL ANALYSIS OF A DIFFERENTIAL OPERATOR WITH AN INVOLUTION AND GENERAL BOUNDARY CONDITIONS ⋮ 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 ⋮ On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations ⋮ Equiconvergence of spectral decompositions for Sturm-Liouville operators: triples of Lebesgue spaces ⋮ Uniform asymptotics of the eigenvalues and eigenfunctions of the Dirac system with an integrable potential ⋮ Completeness property of one-dimensional perturbations of normal and spectral operators generated by first order systems ⋮ Riesz basis property of Hill operators with potentials in weighted spaces ⋮ The Dirac operator with complex-valued summable potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigensystem of an \(L ^{2}\)-perturbed harmonic oscillator is an unconditional basis
• On the completeness of the root vectors of first-order systems
• Spectral expansions of one-dimensional periodic Dirac operators
• Theorem of completeness for a Dirac-type operator with generalized \(\lambda \)-depending boundary conditions
• Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps.
• Spectral triangles of Schrödinger operators with complex potentials
• Equiconvergence theorems for differential operators
• Instability zones of a periodic 1D Dirac operator and smoothness of its potential
• Discontinuities in Dirac eigenfunction expansions
• Riesz basis of root vectors of a non-symmetric system of first-order ordinary differential operators and application to inverse eigenvalue problems
• Theory of Sobolev Multipliers
• Bari–Markus property for Riesz projections of 1D periodic Dirac operators
• ON THE BASIS PROBLEM OF THE EIGENFUNCTIONS OF AN ORDINARY DIFFERENTIAL OPERATOR
• 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
• Instability zones of periodic 1-dimensional Schrödinger and Dirac operators
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform
• Completeness theorems for systems of differential equations

This page was built for publication: Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions