Fractional Differentiation Operator over an Infinite Extension of a   Local Field
  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. 
Anatoly N. Kochubei (Institute of Mathematics, Kiev, Ukraine)