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

Marat V. Markin

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.