Fractional Differentiation Operator over an Infinite Extension of a Local Field
Abstract
Description
We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a representation in the form of a hypersingular integral operator is obtained. It is also shown that the corresponding diffusion measure is not absolutely continuous with respect to the Gaussian measure.
13 pages, AMS-LaTex
13 pages, AMS-LaTex