# Introduction

Chapter

## Abstract

Differential equations containing values of unknown functions and their derivatives at different points of a manifold are called where

*nonlocal differential equations*. The simplest equation of this type has the form$$
D_1 u\left( x \right) + D_2 u\left( {g\left( x \right)} \right) = f\left( x \right),x \in \Omega ,
$$

*D*_{1}and*D*_{2}are some differential operators,*u*is the unknown function, and*g*: Ω → Ω is a self-mapping of the domain where the equation is considered. We shall consider only equations in which the mapping*g*is invertible.## Keywords

Nonlocal Boundary Chern Character Index Formula Toric Manifold Hilbert Module
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Copyright information

© Birkhäuser Verlag AG 2008