%0 Journal Article
%T Harmonic analysis on local fields and adelic spaces I
%A D. V. Osipov
%A A. N. Parshin
%J Mathematics
%D 2007
%I arXiv
%R 10.1070/IM2008v072n05ABEH002424
%X We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.
%U http://arxiv.org/abs/0707.1766v3