1D dirac operators with special periodic potentials
Djakov, Plamen Borissov and Mityagin, Boris Samuel (2012) 1D dirac operators with special periodic potentials. Bulletin of the Polish Academy of Sciences - Mathematics, 60 (1). pp. 59-75. ISSN 0239-7269 (Print) 1732-8985 (Online)
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Official URL: http://dx.doi.org/10.4064/ba60-1-5
For one-dimensional Dirac operators of the form Ly=i(100−1)dydx+vy, v=(0QP0),y=(y1y2),x∈R, we single out and study a class X of π-periodic potentials v whose smoothness is determined only by the rate of decay of the related spectral gaps γn=|λ+n−λ−n|, where λ±n are the eigenvalues of L=L(v) considered on [0,π] with periodic (for even n) or antiperiodic (for odd n) boundary conditions.
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