Work

Global solutions for systems of strongly invariant operators on closed manifolds

Year: 2026

Type: article

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.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17558

Authors: Alexandre Kirilov, Wagner de Moraes, Pedro Tokoro

Institution: Universidade Federal do Paraná

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico