Dynamics of Partial Differential Equations

Volume 1 (2004)

Number 2

Spectral expansions of one-dimensional periodic Dirac operators

Pages: 125 – 191

DOI: http://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 Lp 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.

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