Operators Commuting with Translation by One-Part II: Differential Operators with Periodic Coefficients

An extension of the theory of differential equations and linear operators, both of which have many applications to engineering and mathematical physics. This memorandum studies representation of operators used to employ perturbation techniques. These techniques were heretofore applicable only to operators with compact resolvents and to nonself adjoint differential operators with periodic coefficients on <>. Conditions are given on the coefficients of these operators that ensure that they be spectral (completely reducible) even though they have continuous spectrum.