1D Dirac Operators with Special Periodic Potentials

摘要

For one-dimensional Dirac operators of the form Ly = i (_0~1 _(-1)~0) (dy)/(dx) + vy, v = (_Q~0 _0~P), y = (_(y2)~(y1)), 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 γ_n = |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.