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arXiv · 1302.4850

Radial Solutions of Non-Archimedean Pseudo-Differential Equations

Anatoly N. Kochubei
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Abstract

We consider a class of equations with the fractional differentiation operator $D^\alpha$, $\alpha >0$, for complex-valued functions $x\mapsto f(|x|_K)$ on a non-Archimedean local field $K$ depending only on the absolute value $|\cdot |_K$. We introduce a right inverse $I^\alpha$ to $D^\alpha$, such that the change of an unknown function $u=I^\alpha v$ reduces the Cauchy problem for an equation with $D^\alpha$ (for radial functions) to an integral equation whose properties resemble those of classical Volterra equations. This contrasts much more complicated behavior of $D^\alpha$ on other classes of functions.

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BibTeXRIS

Anatoly N. Kochubei. 2013-02-20. Radial Solutions of Non-Archimedean Pseudo-Differential Equations. https://doi.org/10.2140/pjm.2014.269.355

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