Analysis and Probability over Infinite Extensions of a Local Field

Details Analysis and Probability over Infinite Extensions of a Local Field Analysis and Probability over Infinite Extensions of a Local Field

1998-07-13

arxiv.org/abs/math/9807062v1

Mathematics

Functional Analysis

24 pages, LaTex; to appear in Potential Analysis

Scientific paper

We consider an infinite extension $K$ of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. $K$ is equipped with an inductive limit topology; its conjugate $\bar{K}$ is a completion of $K$ with respect to a topology given by certain explicitly written seminorms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on $\bar{K}$. If we deal with Galois extensions then all these objects are Galois-invariant.

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