Analyse harmonique sur le graphe de Pascal

TL;DR

This paper establishes a spectral decomposition theorem for the Pascal graph, its quotients, and a compactification, advancing understanding of spectral properties in self-similar and quotient graphs.

Contribution

It introduces a spectral decomposition framework for the Pascal graph and related structures, extending spectral analysis to quotient and compactified versions.

Findings

Spectral decomposition theorem proven for Pascal graph

Extension of spectral analysis to quotient graphs

Spectral properties characterized for compactifications

Abstract

We prove a spectral decomposition theorem for a well-known self-similar graph, for some finite graphs which are quotients of this graph and for a compactification of it.