 
Summary: SOME PROBLEMS IN LOCAL HARMONIC ANALYSIS
JAMESARTHUR
University of Toronto
The purpose of this article is to discuss some questions in the harmonic
analysis of real and padic groups. We shall be particularly concerned with
the properties of a certain family of invariant distributions. These distri
butions arose naturally in a global context, as the terms on the geometric
side of the trace formula. However, they are purely local objects, which
include the ordinary invariant orbital integrals. One of our aims is to de
scribe how the distributions also arise in a local context. They appear as
the terms on the geometric side of a new trace formula, which is simpler
than the original one, and is the solution of a natural question in local har
monic analysis. The local trace formula seems to be a promising tool. It
plight have implications for the difficult local problems which are holding
up progress in automorphic forms.
We have organized the paper loosely around three general problems.
We shall describe the problems and the distributions together in $1. This
section is entirely expository. In $2,which is also largelyexpository, we shall
discuss the role of the distributions in the local trace formula. Finally, in $3,
we shall see how the local trace formula can be applied to some questions
