A new proof of the Lie-Trotter-Kato formula in Hadamard spaces

TL;DR

This paper presents a simpler proof of the Lie-Trotter-Kato formula in Hadamard spaces, replacing complex ultrapower techniques with weak convergence methods, thus making the proof more accessible.

Contribution

It provides a more straightforward proof of the Lie-Trotter-Kato formula in Hadamard spaces using weak convergence instead of ultrapower techniques.

Findings

Simplified proof of the Lie-Trotter-Kato formula in Hadamard spaces

Replaces ultrapower technique with weak convergence

Enhances accessibility of the proof

Abstract

The Lie-Trotter-Kato product formula has been recently extended into Hadamard spaces by [Stojkovic, Adv. Calc. Var., 2012]. The aim of our short note is to give a simpler proof relying upon weak convergence instead of an ultrapower technique.