Take the tour ×   Where goes a characterictic $0$ person, in
order to learn about the local harmonic analysis for local
fields in characteristic $p$? Is there nice and conscise
reference for the local fields in positive characteristic.
Something conscise like Sally's survey, which is for
characterictic zero only:
http://www.springerlink.com/content/g45268h62705h470/  It should
contain some of these: the additive and multiplicative Fourier
transform, the Haarmeasures, the Gamma functions, etc.
share|improve this question add comment  1 Answer  up vote 5
down vote accepted  Harmonic analysis dealing with complex-
valued functions on a local field $K$ depends very little on the
characteristic of $K$ and can be given in the general case, for
an arbitrary $K$. See  I. M. Gelfand, M. I. Graev, and I. I.
Piatetski-Shapiro, Representation Theory and Automorphic
Functions, Saunders, Philadelphia, 1969.  For some more recent
results see also  A. N. Kochubei, Pseudo-Differential Equations
and Stochastics over Non-Archim