Fredholm Properties of Elliptic Operators on ${\mathbb{R}}^n$

Abstract

We study the Fredholm properties of a general class of elliptic differential operators on ${\mathbb{R}}^n$. These results are expressed in terms of a class of weighted function spaces, which can be locally modeled on a wide variety of standard function spaces, and a related spectral pencil problem on the sphere, which is defined in terms of the asymptotic behaviour of the coefficients of the original operator.

AMS-LaTeX, 61 pages