On the generation of Beurling type Carleman ultradifferentiable   $C_0$-semigroups by scalar type spectral operators
  A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable $C_0$-semigroups is established, the important case of the Gevrey ultradifferentiability is considered in detail, the implementation of the general criterion corresponding to a certain rapidly growing defining sequence is observed. 
Marat V. Markin
math.FA