The Plancherel Formula, the Plancherel Theorem, and the Fourier transform of orbital integrals

TL;DR

This paper explores different formulations of the Plancherel Formula and Theorem for reductive groups over local fields, providing insights into their structure and applications in harmonic analysis.

Contribution

It systematically analyzes various forms of the Plancherel formulas and theorems specific to reductive groups over local fields, clarifying their relationships and implications.

Findings

Different forms of the Plancherel Formula are characterized.

Connections between the Plancherel Theorem and harmonic analysis are elucidated.

Applications to orbital integrals are discussed.

Abstract

We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.