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arXiv · 2005.11166

Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform

Anatoly N. Kochubei
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Abstract

In an earlier paper (A. N. Kochubei, {\it Pacif. J. Math.} 269 (2014), 355--369), the author considered a restriction of Vladimirov's fractional differentiation operator $D^\alpha$, $\alpha >0$, to radial functions on a non-Archimedean field. In particular, it was found to possess such a right inverse $I^\alpha$ that the appropriate change of variables reduces equations with $D^\alpha$ (for radial functions) to integral equations whose properties resemble those of classical Volterra equations. In other words, we found, in the framework of non-Archimedean pseudo-differential operators, a counterpart of ordinary differential equations. In the present paper, we begin an operator-theoretic investigation of the operator $I^\alpha$, and study a related analog of the Laplace transform.

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Anatoly N. Kochubei. 2020-05-21. Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform. https://arxiv.org/abs/2005.11166

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