Global solutions for systems of strongly invariant operators on closed manifolds
Abstract
We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential operator, which provides a spectral decomposition of L 2 ( M ) L^2(M) into finite-dimensional eigenspaces. This framework allows us to characterize these global properties through asymptotic estimates on the matrix symbols of the operators. Additionally, for systems of normal strongly invariant operators, we derive an explicit solution formula and establish sufficient conditions for global hypoellipticity and solvability in terms of their eigenvalues.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Holomorphic and Operator Theory
Advanced Operator Algebra Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 154
- Issue
- 3
- Pages
- 1295–1310
- Publication date
- 14 January 2026
- Language
- EN