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arXiv · 1502.02462

Summable solutions of some partial differential equations and generalised integral means

Sławomir Michalik
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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.

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Sławomir Michalik. 2015-02-09. Summable solutions of some partial differential equations and generalised integral means. https://doi.org/10.1016/j.jmaa.2016.07.031

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