Harmonic analysis on local fields and adelic spaces II

TL;DR

This paper advances harmonic analysis on local fields and adelic spaces related to arithmetical surfaces, providing structure theorems for their quotients within filtered abelian groups and vector spaces over R or C.

Contribution

It develops harmonic analysis in categories of filtered abelian groups and vector spaces, specifically applied to local fields and adelic spaces from arithmetical surfaces, with new structure theorems.

Findings

Proven structure theorems for quotients of adelic groups

Development of harmonic analysis in new categorical frameworks

Application to local fields and adelic spaces from arithmetical surfaces

Abstract

This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These categories contain as objects local fields and adelic spaces arising from arithmetical surfaces. Some structure theorems are proven for quotients of the adelic groups of algebraic and arithmetical surfaces.