English

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 C2C_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.

Keywords

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

R2 v1 2026-06-21T08:57:32.668Z