International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 9, Pages 555-563
On an abstract evolution equation with a spectral operator of scalar type
Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston 02215, MA, USA
Received 20 December 2001
Copyright © 2002 Marat V. Markin. 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.
It is shown that the weak solutions of the evolution equation , , where is a spectral operator of scalar type in a complex Banach space , defined by Ball (1977), are given by the formula , , with the exponentials understood in the sense of the operational calculus for such operators and the set of the initial values, 's, being , that is, the largest possible such a set in .