Abstract
Various results concerning the smoothness of gap boundaries for
Harper type operators are extended to a large class of "twisted integral
operatos" in $L^2(Z^2)$. The results hold true also for analogous classes
of operators in $L^2(R^n)$ and imply the fact that the gap boundaries for
magnetic Schrodinger and Dirac operators are, up to a logarithmic factor,
Lipschitz continuous in the magnetic field strenght.
The proofs are based on gauge covariance and magnetic perturbation
theory
Contact person:Arne Jensen.