Introduction to the Rapid Decay property

TL;DR

This paper introduces the Rapid Decay property, surveys known results and equivalent definitions, and discusses the special case when G equals Z, providing a comprehensive overview for researchers.

Contribution

It offers a clear, accessible introduction and survey of the Rapid Decay property, consolidating various known results and definitions.

Findings

Summarizes known results on the Rapid Decay property

Provides equivalent definitions of the property

Analyzes the case when G equals Z in detail

Abstract

This is an introduction to the Rapid Decay property, with a survey of known results and equivalent definitions of this property. We also discuss in details the easy case when G = Z. Everything in this paper is well-known by different sets of people.