Global ultradifferentiable hypoellipticity on compact manifolds

TL;DR

This paper investigates the global hypoellipticity of linear operators within Komatsu classes on compact manifolds, using eigenfunction expansions and matrix-symbol analysis to characterize these spaces.

Contribution

It introduces a novel approach combining eigenfunction expansion characterization with matrix-symbol analysis for hypoellipticity in Komatsu classes.

Findings

Characterization of Komatsu classes via eigenfunction expansions.

Analysis of matrix-symbols related to hypoellipticity.

Framework applicable to elliptic operators on compact manifolds.

Abstract

We study the global hypoellipticity problem for certain linear operators in Komatsu classes of Roumieu and Beurling type on compact manifolds. We present an approach by combining a characterization of these spaces via eigenfuction expansions, generated by an elliptic operator, and the analysis of matrix-symbols obtained by these expansions.