Elliptic theory for operators associated with diffeomorphisms of smooth manifolds

TL;DR

This paper surveys the elliptic theory for operators linked to diffeomorphisms on smooth manifolds, covering classical and recent results relevant to analysis, geometry, and physics.

Contribution

It provides a comprehensive overview and detailed formulations of the key results in elliptic theory related to diffeomorphism-associated operators.

Findings

Classical results on elliptic operators are summarized

Recent advancements in the field are discussed

The survey connects analysis, geometry, and physics applications

Abstract

In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as results obtained recently. The paper consists of an introduction and three sections. In the introduction we give a general overview of the area of research. For the reader's convenience here we tried to keep special terminology to a minimum. In the remaining sections we give detailed formulations of the most important results mentioned in the introduction.