Hi,


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.



Harmonic Analysis for Function Fields
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-Archimedean Fields, Marcel Dekker, New York, 2001.


However, if one is interested in analysis of functions $K\to K$, the theory in positive characteristic is completely different from the $p$-adic case. See


A. N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009. 


