On perturbation of differential operators
Kandiah Dayanithy · Pacific Journal of Mathematics · 1975
The theory of spectral operators, when applied to eigenfunction expansions, covers the unconditionally convergent case.However, by perturbing certain spectral differential operators, J. Schwartz has obtained differential operators which are not spectral but whose eigenfunctions span the whole space.In this paper we show how new norms can be constructed so as to make these perturbed differential operators spectral.This we achieve by showing that such operators have an underlying generalized spectral measure (as defined by V. E. Ljance) and that every generalized spectral measure is essentially a C-spectral measure.