A taylor-like expansion of a commutator with a function of self-adjoint, pairwise commuting operators - Rasmussen, Morten Grud (MATHEMATICA SCANDINAVICA, 2012)
Let A be a u-vector of self-adjoint, pairwise commuting operators and B a bounded operator of class C^n_0(A). We prove a Taylor-like expansion of the commutator [B,f(A)] for a large class of functions fR^ u→R, generalising the one-dimensional result where A is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.