Harmonic Analysis on the Ad\`ele Ring of $\Q$
Classical Analysis and ODEs
2018-03-20 v2
Abstract
The ring of finite ad\`eles of the rational numbers is obtained in this article as a completion of with respect to a certain non--Archimedean metric. This ultrametric allows to represent any finite ad\`ele as a series generalizing --adic analysis. The description made provides a new perspective for the adelic Fourier analysis on , which also permits to introduce new oscillatory integrals. By incorporating the infinite prime, the mentioned results are extended to the complete ring of ad\`eles } of .
Keywords
Cite
@article{arxiv.1803.01964,
title = {Harmonic Analysis on the Ad\`ele Ring of $\Q$},
author = {Victor A. Aguilar-Arteaga and Manuel Cruz-López and Samuel Estala-Arias},
journal= {arXiv preprint arXiv:1803.01964},
year = {2018}
}
Comments
27 pages, 1 figure