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

2024/08/29 by Anatoly N. Kochubei, Kochubei, Anatoly N., Mariia V. Serdiuk +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Analysis #Numerical methods for differential equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.00136

openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L¹-estimate.

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