FREDHOLMNESS VS. SPECTRAL DISCRETENESS FOR FIRST-ORDER DIFFERENTIAL OPERATORS

摘要

It is shown that for essentially self-adjoint first-order differential operators D, acting on sections of bundles over complete (non-compact) manifolds, Fredholmness vs. Spectral Discreteness is the same as 'there exists c > 0, D is c-invertible at infinity' vs. 'for all c > 0, D is c-invertible at infinity'. An application involving the spectral theory of electromagnetic Dirac operators is then given.