International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 57-60, 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
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.