REPRODUCING KERNEL HILBERT SPACES

Fundamental to all of our research is that of Reproducing Kernel Hilbert Spaces (RKHS). Each RKHS corresponds to a unique positive definite kernel function, which intertwines data (or centers) with function theoretic operators in many nontrivial ways. The development of new RKHSs in our group has paved the way to new numerical methods for fractional order systems, allowed for the direct DMD analysis of higher order dynamical systems, and resolved open questions in pure mathematics such as whether there is a RKHS that has only trivial densely defined multiplication operators.

Reproducing Kernels and Complex Function Theory

Densely Defined Operators and RKHS

Data Science and RKHS