Year: 2025
Type: article
Abstract: We discuss explicit approximations of uniformly continuous functions by Lipschitz continuous functions. Such constructions are relevant in the analysis of Toeplitz operators. As model cases, we treat $${\mathbb {C}}^n$$ C n with the Euclidean metric and the complex unit ball $${\mathbb {B}}^n$$ B n equipped with the Bergman metric in details. In both cases a flow of approximating real analytic Lipschitz functions with a control of the Lipschitz constants is defined. We provide two applications of these results to semi-commutator estimates in Berezin Toeplitz quantization as well as to the analysis of certain $$C^*$$ C ∗ algebras generated by Toeplitz operators on the complex unit ball $${\mathbb {B}}^2.$$ B 2 .
Author: Wolfram Bauer
Institution: Leibniz University Hannover
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4413290186