Multicentric holomorphic calculus for $n-$tuples of commuting operators

Abstract

‎‎In multicentric holomorphic calculus‎, ‎one represents the function $\varphi$‎, ‎using a new polynomial variable $w=p(z),$ $z\in \mathbb{C},$ in such a way that when it is evaluated at the operator $T,$ then $p(T)$ is small in norm‎. ‎Usually it is assumed that $p$ has distinct roots‎. ‎In this paper we aim to extend this multicentric holomorphic calculus to $n$-tuples of commuting operators looking in particular at the case when $n=2$‎.