Fredholm Properties of Elliptic Operators on $\R^n$
  We study the Fredholm properties of a general class of elliptic differential operators on $\R^n$. 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. 
Daniel M. Elton (University of Sussex, Brighton, UK)