Parabolic-type pseudodifferential equations with elliptic symbols in dimension 3 over $p$-adics

Abstract

In this paper we deal with the operator defined as 𝑓(∂,𝛼)𝜙:=−1𝜉→𝑥(|𝑓(𝜉)|𝛼𝑝𝑥→𝜉𝜙), where f(ξ) is an elliptic quadratic form of dimension 3 over ℚ p . We study the Cauchy problem associated that operator, and find the fundamental solution and some properties of it, using the techniques given by Kochubei.

Oscar F. Casas

Associate Professor