Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces

TL;DR

This paper characterizes Gevrey ultradifferentiable functions and their duals on compact Lie groups and homogeneous spaces using representation theory and spectral analysis, providing a comprehensive framework for these function spaces.

Contribution

It offers new global characterizations of Gevrey spaces and ultradistributions on compact Lie groups and homogeneous spaces via spectral and representation-theoretic methods.

Findings

Characterization of Gevrey-Roumieu and Gevrey-Beurling spaces on compact Lie groups.

Dual space descriptions in terms of ultradistributions.

Extension of characterizations to compact homogeneous spaces.

Abstract

In this paper we give global characterisations of Gevrey-Roumieu and Gevrey-Beurling spaces of ultradifferentiable functions on compact Lie groups in terms of the representation theory of the group and the spectrum of the Laplace-Beltrami operator. Furthermore, we characterise their duals, the spaces of corresponding ultradistributions. For the latter, the proof is based on first obtaining the characterisation of their $\alpha$-duals in the sense of Koethe and the theory of sequence spaces. We also give the corresponding characterisations on compact homogeneous spaces.