G-Convergence of Dirac Operators
Copyright policy )G-Convergence of Dirac Operators
We consider the linear Dirac operator with a (-1)-homogeneous locally periodic potential that varies with respect to a small parameter. Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove G-compactness in the strong resolvent sense for families of projections of Dirac operators. We also prove convergence of the corresponding point spectrum in the spectral gap.
13 pages
- Chalmers University of Technology Sweden
- University of Gothenburg Sweden
Linear operator approximation theory, G-convergence, Perturbation theory of linear operators, Methods involving semicontinuity and convergence; relaxation, Dirac operator, General topics in linear spectral theory for PDEs, G-compactness, Homogenization in context of PDEs; PDEs in media with periodic structure, point spectrum, Functional Analysis (math.FA), Mathematics - Functional Analysis, Time-dependent Schrödinger equations and Dirac equations, spectral gap, QA1-939, FOS: Mathematics, Mathematics
Linear operator approximation theory, G-convergence, Perturbation theory of linear operators, Methods involving semicontinuity and convergence; relaxation, Dirac operator, General topics in linear spectral theory for PDEs, G-compactness, Homogenization in context of PDEs; PDEs in media with periodic structure, point spectrum, Functional Analysis (math.FA), Mathematics - Functional Analysis, Time-dependent Schrödinger equations and Dirac equations, spectral gap, QA1-939, FOS: Mathematics, Mathematics
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