Smoothness of Heat Kernel Measures on Infinite-Dimensional Heisenberg-Like Groups

TL;DR

This paper investigates measures linked to Brownian motions on infinite-dimensional Heisenberg-like groups, demonstrating that both the path space measure and heat kernel measure exhibit strong smoothness properties.

Contribution

It establishes the smoothness of measures related to Brownian motions on infinite-dimensional Heisenberg-like groups, a novel result in this mathematical setting.

Findings

Proves strong smoothness of path space measure.

Shows heat kernel measure is smooth.

Extends understanding of infinite-dimensional stochastic analysis.

Abstract

We study measures associated to Brownian motions on infinite-dimensional Heisenberg-like groups. In particular, we prove that the associated path space measure and heat kernel measure satisfy a strong definition of smoothness.