Dynamics of Partial Differential Equations

Volume 1 (2004)

Number 2

Spectral expansions of one-dimensional periodic Dirac operators

Pages: 125 – 191

DOI: https://dx.doi.org/10.4310/DPDE.2004.v1.n2.a1

Author

Boris Mityagin (Department of Mathematics, The Ohio State University, Columbus, Ohio, U.S.A.)

Abstract

We study localization of spectra (Counting Lemma) and L^p convergence of spectral decompositions of 1D periodic Dirac operators. The main technical tool is estimates of the resolvent norms in their dependence on the smoothness of a potential.

Keywords

Dirac operator, resolvent, spectral decompositions, uniform and unconditional convergence

2010 Mathematics Subject Classification

Primary 34L40, 42C15. Secondary 47E05.

Published 1 January 2004