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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 3, Pages 475-482

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 Hindawi Publishing Corporation. 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.


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 dΓ1dΓ2 as λ.