International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 60, Pages 3219-3235
On the Carleman classes of vectors of a scalar type spectral operator
Department of Partial Differential Equations, Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Street, Kiev 01601, Ukraine
Received 6 November 2003
Copyright © 2004 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.
The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator's resolution of the identity. A theorem of the Paley-Wiener type is considered as an application.