1D dirac operators with special periodic potentials

Abstract

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.