Satellite mini-conference "Analysis and Probability"
Kontakt: yacin [dot] ameur [at] math [dot] lu [dot] se
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1. 14.00-14.55: Tomas Sjödin (Linköping): "Some Extremal Problems for Harmonic Vector Fields"
2. 15.15-16.10: Maurice Duits (KTH), TBA
1. Sjödin: Harmonic vector fields is a natural generalization of analytic (or, to be more precise, anti-analytic) functions to higher dimensions.
The aim of this talk is to discuss recent progress on upper and lower bounds of the distance $\lambda_p(\Omega)$ between the space of these harmonic vector fields on a smooth bounded subset $\Omega$ of $n$-dimensional Euclidean space and the identity in the $L^p$ norm. The quantity $\lambda_p(\Omega)$ is called the Bergman analytic content (simply analytic content if $p=\infty$).
We will survey the results, with a particular focus on the case $p=\infty$, and give some ideas of the proofs, which involve both a potential-theoretic construction called partial balayage, as-well as results from the theory of optimal transport.
The talk is based on joint work with S.J. Gardiner and M. Ghergu.