An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups

TL;DR

This paper explores the relationship between limit-periodic potentials in Schrödinger operators and procyclic profinite groups, classifying their hulls and illustrating how these potentials can be generated from such groups.

Contribution

It provides a comprehensive exposition linking limit-periodic potentials with profinite groups, including classification of hulls and generation methods, advancing understanding in spectral theory.

Findings

Hulls of limit-periodic potentials are procyclic groups

Limit-periodic potentials can be generated from procyclic groups

Reviewed recent results on Schrödinger operators in this context

Abstract

We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schroedinger operators obtained in this context.