Global hypoellipticity of systems of Fourier multipliers on compact Lie groups
Abstract
Abstract In parallel to the characterization of global hypoellipticity for G -invariant operators on homogeneous vector bundles obtained by Cardona and the author [J. Pseudo-Differ. Oper. Appl. 16, 23 (2025)], in this paper we obtain necessary and sufficient conditions for an arbitrary system of left-invariant operators on a compact Lie group to be globally hypoelliptic, via a proof which avoids the homogeneous vector bundle structure of that paper. We then prove alternative sufficient conditions for globally hypoellipticity for a large class of systems making use of lower bounds for the smallest singular value of complex matrices.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- Journal of Pseudo-Differential Operators and Applications
- Volume
- 17
- Issue
- 2
- Publication date
- 11 March 2026
- Language
- EN