Uniform doubling for abelian products with $\operatorname{SU}(2)$

TL;DR

This paper proves the uniform doubling property for Lie groups formed as quotients of SU(2) times Euclidean space, impacting analysis and spectral theory of heat kernels on these groups.

Contribution

It establishes the uniform doubling property for a broad class of Lie groups including non-compact and compact types, extending previous results.

Findings

Uniform doubling holds for quotients of SU(2) times Euclidean space

Includes the four-dimensional unitary group U(2)

Implications for heat kernel analysis and spectral properties

Abstract

We prove that the uniform doubling property holds for every Lie group which can be written as a quotient group of $\operatorname{SU}(2) \times \mathbb{R}^n$ for some $n$. In particular, this class includes the four-dimensional unitary group $\operatorname{U}(2)$. As this class contain non-compact as well as compact Lie groups, we discuss a number of analytic and spectral consequences for the corresponding heat kernels.