Solvability of invariant systems of differential equations on H2$\mathbb {H}^2$ and beyond

<jats:title>Abstract</jats:title> <jats:p>We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non‐compact type can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis–Malgrange theorem. We get complete solvability for the hyperbolic plane and partial results for products and the hyperbolic 3‐space .</jats:p>