International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 60, Pages 3219-3235
doi:10.1155/S0161171204311117

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

Abstract

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.