Solvability of invariant systems of differential equations on H2 H² and beyond

Key Points

• This research aims to explore the solvability of invariant systems of differential equations using Fourier transforms in non-compact symmetric spaces.
• Utilized Fourier transform techniques for distributional sections of vector bundles.
• Established connections to Hörmander's proof of the Ehrenpreis–Malgrange theorem.
• Analyzed systems of differential equations specifically in the hyperbolic plane and hyperbolic 3-space.
• Achieved complete solvability for invariant differential equations on the hyperbolic plane.
• Obtained partial solvability results for invariant equations on hyperbolic 3-space and products of symmetric spaces.