Summable solutions of some partial differential equations and generalised integral means
arXiv:1502.02462 · doi:10.1016/j.jmaa.2016.07.031
Abstract
We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisation of summability of formal power series solutions to some multidimensional partial differential equations in terms of holomorphic properties of generalised integral means of the Cauchy data.
20 pages