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 $L^2(M)$ 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.

References in corpus (6)

• Global hypoellipticity and global solvability for vector fields on compact Lie groups
• Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields
• Partial Fourier series on compact Lie groups
• Global regularity and solvability of left-invariant differential systems on compact Lie groups
• Global Hypoellipticity for Strongly Invariant Operators
• Global hypoellipticity of sums of squares on compact manifolds