P-adic Elliptic Quadratic Forms, Parabolic-Type Pseudodifferential Equations With Variable Coefficients, and Markov Processes

Abstract: In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four dimensional vector space over the field of p-adic numbers.