Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations

Anatoly N. Kochubei; Mariia V. Serdiuk

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arXiv · 2409.00136

Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations

Anatoly N. Kochubei·Mariia V. Serdiuk

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Abstract

In this paper we study a new class of pseudo-differential equations on functions of two $p$-adic variables. It is proved that the correspondent Cauchy problem has a unique solution. Some properties of this solution are studied, in particular, the finite dependence property and an $L^1$-estimate.

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Anatoly N. Kochubei, Mariia V. Serdiuk. 2024-08-29. Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations. https://arxiv.org/abs/2409.00136

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