The Invariant Trace Formula. I. Local Theory

Some Problems in Local Harmonic Analysis

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 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 invar...

The Invariant Trace Formula. Ii. Global Theory

The purpose of this article is to prove an explicit invariant trace formula. In the preceding paper [1 (j)], we studied two families of invariant distributions. Now we shall exhibit these distributions as terms on the two sides of the invariant trace formula. We refer the reader to the introduction of [l (j)], which contains a general discussion of the problem. In this introduction, we shall de...

The Invariant Trace Formula . 11 . Global Theory

The purpose of this article is to prove an explicit invariant trace formula. In the preceding paper [l(j)] , we studied two families of invariant distributions. Now we shall exhibit these distributions as terms on the two sides of the invariant trace formula. We refer the reader to the introduction of [1 (j)], which contains a general discussion of the problem. In this introduction, we shall de...

Continuous symmetry reduced trace formulas

Trace formulas relate short time dynamics (unstable periodic orbits) to long time invariant state space densities (natural measure). Higher dimensional dynamics requires inclusion of higherdimensional compact invariant sets, such as partially hyperbolic invariant tori, into trace formulas. A trace formula for a partially hyperbolic (N +1)-dimensional compact manifold invariant under a global co...

The Iny Ariant Trace Formula . I . Local Theory