International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 475-482
doi:10.1155/S0161171297000641
On the growth of the spectral measure
King Fahd University of Petroleum and Minerals, Department of Mathematical Sciences, Dhahran 31262, Saudi Arabia
Received 26 May 1992; Revised 12 June 1996
Copyright © 1997 A. Boumenir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We are concerned with the asymptotics of the spectral measure associated with a
self-adjoint operator. By using comparison techniques we shall show that the eigenfunctionals of
L2 are close to the eigenfunctionals L1 if and only if dΓ1≈dΓ2 as λ→∞.