Divided Differences in Noncommutative Geometry: Rearrangement Lemma, Functional Calculus and Expansional Formula

Understand

We state a generalization of the Connes-Tretkoff-Moscovici Rearrangement Lemma and give a surprisingly simple (almost trivial) proof of it.

• Secondly, we put on a firm ground the multivariable functional calculus used implicitly in the Rearrangement Lemma and elsewhere in the recent modular curvature paper by Connes and Moscovici.
• Furthermore, we show that the fantastic formulas connecting the one and two variable modular functions of loc.
• cit.