A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field

Abstract

In this paper, we will present a method to construct a spatially inhomogeneous process on the p-adic number field. Secondly, we will modify the definition of the derivative of real-valued function on the field, hinted by the Fourier transformation. As a result, we can introduce a class of spatially inhomogeneous modified stable processes, which cannot be obtained by the transformation by multiplicative functional. Lastly, recurrence and transience criteria for the non-local Dirichlet spaces will be presented.