ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Boris Mityagin (Ohio State University)
Spectra, instability zones and spectral expansions of 1D periodic Dirac operators

Abstract: We analyze localization of spectra of 1D periodic Dirac operators (Counting Lemma) and the rates of decay of their spectral gaps. Further, the series of results on convergence and divergence of spectral decompositions associated with 1D Dirac operators will be presented. This talk is based on the following recent publications.

1. B.Mityagin, Spectral decompositions of 1D periodic Dirac operators, Doklady, 393:4 (2003); English: Sov. Doklady, 68:4 (2003).
2. P.Djakov and B.Mityagin, Spectra of 1D periodic Dirac operators and smoothness of potentials, C.R. Math. Rep. Acad. Sci. Canada, 25(4), (2003), 121- 125.
3. P.Djakov and B.Mityagin, The asymptotics of spectral gaps of 1D Dirac operator with cosine potential, Letters Math. Phys. 65 (2003), 95 - 108.
4. B.Mityagin, Spectral expansions of one-dimensional periodic Dirac operators, Dynamics of Partial Differential Equations, vol.1, Summer 2004, to appear.