Polynomial estimates for c-functions on reductive symmetric spaces

TL;DR

This paper demonstrates that c-functions associated with reductive symmetric spaces are bounded polynomially in imaginary directions, providing new estimates crucial for harmonic analysis on these spaces.

Contribution

It establishes polynomial bounds for c-functions in imaginary directions, advancing understanding of their growth behavior in harmonic analysis.

Findings

C-functions satisfy polynomial bounds in imaginary directions

Provides new estimates for harmonic analysis on reductive symmetric spaces

Enhances understanding of c-function growth behavior

Abstract

The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.