Analysis and probability over infinite extensions of a local field (Q1301763)

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 \(K\) is a completion of \(K\) with respect to a topology given by certain explicitly written semi-norms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on \(K\). If we deal with Galois extensions then all these objects are Galois-invariant.