Vol. 57, No. 1, 1975

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On perturbation of differential operators

Kandiah Dayanithy

Vol. 57 (1975), No. 1, 85–89

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. È. Ljance) and that every generalized spectral measure is essentially a C-spectral measure.

Mathematical Subject Classification 2000
Primary: 47B40
Received: 3 June 1974
Revised: 26 November 1974
Published: 1 March 1975
Kandiah Dayanithy