Smooth approximations to solutions of perturbed Weyl and Dirac equations

Iterations of spherical mean values of the initial condition are used to approximate solutions of the Weyl and the Dirac equations in the Hilbert space $[L^2(\mathbb R^n)]^N$ . In this work we smooth the potential and the initial condition, without restrictions on the increase rate as $\|x\|\to\infty$. By iterating perturbations of such mean values, we prove apriori estimates for the approximate solutions of the perturbed Weyl and Dirac equations in the topology of uniform convergence of time and space derivatives on compact subsets in $\mathbb R\times\mathbb R^n$.