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Some Problems in Local Harmonic Analysis

  • James Arthur
Chapter
Part of the Progress in Mathematics book series (PM, volume 101)

Abstract

The purpose of this article is to discuss some questions in the harmonic analysis of real and p-adic groups. We shall be particularly concerned with the properties of a certain family of invariant distributions. These distributions 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 describe 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 harmonic analysis. The local trace formula seems to be a promising tool. It might have implications for the difficult local problems which are holding up progress in automorphic forms.

Keywords

Parabolic Subgroup Trace Formula Automorphic Form Invariant Distribution Levi Subgroup 
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.

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • James Arthur
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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