| Speaker: Dr Bernhard Haak Affiliation: University of Bordeaux Time: 11:00 Friday, 29 March, 2019 Location: 303-257 |
| In this talk we will first review the definition of an (generally unbounded) operator having a bounded $H^\infty$ calculus, and explain why and how this functional calculus is naturally linked to square functions as they appear in classical harmonic analysis. This theory has first been developed my Alan McIntosh and coworkers for operators on Hilbert spaces and was later extended to a Banach space setting by Kalton and Weis. In the joint work with Markus Haase (Kiel, Germany) that is subject of my talk, we explain the Kalton-Weis theory in short and concise way, using essentially two techniques: a first, an elementary step to get "starting point" square functions, and then a powerful integral representation theorem that, bootstrapping from the first step, allows to recover the entire theory. It turns out that the vector-valued square functions we consider behave themselves as a kind of functional calculus, so that the passage from functional calculus to square functions (and back) can be read as the transfer from one functional calculus to another. (joint work with M. Haase). |