arXiv subjects

Victor A. Aguilar-Arteaga

Publications and source records attributed to Victor A. Aguilar-Arteaga.

3 recordsLinked to original sources

arXiv2026

An equichordal characterization of the ellipsoid and the sphere

Let $K$ and $L$ be two convex bodies in $\mathbb R^n$, $n\geq 3$, with $L\subset \text{int}\, K$. In this paper we prove the following result: if every two parallel chords of $K$, supporting $L$ have the same length, then $K$ and $L$ are homothetic and concentric ellipsoids. We also prove a similar theorem when instead of parallel chords we consider concurrent chords. We may also replace, in both theorems, supporting chords of $L$ by supporting sections of constant width. In the last section we also prove similar theorems where we consider projections instead of sections.

math.MG↗

arXiv2018

Harmonic Analysis on the Adèle Ring of $\Q$

The ring of finite adèles $\Af$ of the rational numbers $\Q$ is obtained in this article as a completion of $\Q$ with respect to a certain non--Archimedean metric. This ultrametric allows to represent any finite adèle as a series generalizing $m$--adic analysis. The description made provides a new perspective for the adelic Fourier analysis on $\Af$, which also permits to introduce new oscillatory integrals. By incorporating the infinite prime, the mentioned results are extended to the complete ring of adèles $\A$} of $\Q$.

math.CA↗

arXiv2017

A Heat Equation on some Adic Completions of Q and Ultrametric Analysis

This article deals with a Markov process related to the fundamental solution of a heat equation on the direct product ring Q_S, where Q_S is a finite direct product of p-adic fields. The techniques developed here are different from the well known ones: they are geometrical and very simple. As a result, the techniques developed here provides a general framework of these problems on other related ultrametric groups.

math.FA↗