Analysis and Probability over Infinite Extensions of a Local Field, II: A Multiplicative Theory

Abstract

Let $V$ be a projective limit, with respect to the renormalized norm mappings, of the groups of principal units corresponding to a strictly increasing sequence of finite separable totally and tamely ramified Galois extensions of a local field. We study the structure of the dual group $V'$, introduce and investigate a fractional differentiation operator on $V$, and the corresponding L\'evy process. Part I: Potential Anal., 10 (1999), 305-325.