On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators

TL;DR

This paper characterizes scalar type spectral generators of Beurling type Carleman ultradifferentiable $C_0$-semigroups, with detailed analysis of the Gevrey case and criteria involving rapidly growing sequences.

Contribution

It provides a new characterization of spectral generators for ultradifferentiable semigroups, especially in the Gevrey case, using criteria based on rapidly growing sequences.

Findings

Characterization of scalar type spectral generators for Beurling type Carleman ultradifferentiable $C_0$-semigroups

Detailed analysis of the Gevrey ultradifferentiability case

Implementation of a criterion involving rapidly growing defining sequences

Abstract

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.