It is shown that for a wide class of linear partial differential operators with constant coefficients the space of real analytic zero solutions does not admit a Schauder basis. This is based on results on the linear topological structure of the space of zero solutions and a careful analysis of the solvability with a real analytic parameter.
"Real analytic zero solutions of linear partial differential operators with constant coefficients." Bull. Belg. Math. Soc. Simon Stevin 14 (3) 577 - 586, September 2007. https://doi.org/10.36045/bbms/1190994220