Christian Emmel: Reproducing Kernel Hilbert Spaces

The aim of this talk is to provide a gentle introduction to the theory of reproducing kernel spaces. Specifically, we will review their definition and basic properties, characterize the occurring kernel functions, and establish a fundamental interpolation result. Furthermore, we will discuss two illustrative examples from complex analysis and statistics, which highlight the widespread use of reproducing kernels in contemporary mathematics.

This talk precedes Damir Filipović colloquium talk  on “Kernel methods with applications in finance and statistics” and is accessible to a broad audience (master and PhD students).