AG Mathematische Physik, Matthias Lesch (Bonn): Rearrangement Lemma, divided differences and the multivariate holomorphic functional calculus

Matthias Lesch (Bonn)

Rearrangement Lemma, divided differences and the multivariate
holomorphic functional calculus

Abstract:
The so called Rearrangement Lemma is a technical device in the
context of heat trace expansions on noncommutative spaces resp. for
operators with noncommutative leading symbol.

A couple of years ago I gave a systematic treatment and discussed the
link to the classical divided difference formalism.

In this talk I would like to recast the issue from the point of view of
the multivariate holomorphic functional calculus.

The latter has a rich history and is of some interest in its own as it
is by no means just a straightforward generalization of the usual
one-variable case. I will review this history and give some elementary
applications to noncommutative versions of Newton interpolation and
Taylor formulas as well as a holomorphic version of the rearrangement lemma.

The talk is based on an ongoing project
with Luiz Hartmann from Sao Carlos, Brazil.