Harmonic analysis on local fields and adelic spaces I
Algebraic Geometry
2009-11-13 v3 Number Theory
Abstract
We develop a harmonic analysis on objects of some category 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.
Cite
@article{arxiv.0707.1766,
title = {Harmonic analysis on local fields and adelic spaces I},
author = {D. V. Osipov and A. N. Parshin},
journal= {arXiv preprint arXiv:0707.1766},
year = {2009}
}
Comments
69 pages; corrected typos and inserted some changes into the last section