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

Published 29 Aug 2024 in math.AP | (2409.00136v1)

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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