Drexel Math Collqouium

Wednesday, April 2, 2025 - 3:00pm to 4:00pm

Hugo Woerdeman

Math Department

Abstract: After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $C^n$, as well as the Hardy space on the polydisk and half-space. In particular, we show how the framework leads to a procedure to find a minimal norm element $f$ satisfying interpolation conditions $f(z_j)=w_j$, $j=1,\ldots , n$. We also explain the techniques in the setting of $\ell^p$ spaces where the norm is defined via a change of variables and provide numerical examples. This talk is based on joint work with Gilbert J. Groenewald and Sanne ter Horst.