Gevrey functions and ultradistributions on compact Lie groups and 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.

arXiv comment23 pages

References in corpus (1)

• Global quantization of pseudo-differential operators on compact Lie groups, SU(2) and 3-sphere

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