Vol. 57, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
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