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.
On the regularity of scalar type spectral $C_0$-semigroups
On a spectral mapping theorem for scalar type spectral operators, the weak spectral mapping theorem for and stability of $C_0$-semigroups of such operators
On asymptotics for $C_0$-semigroups
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