### Advanced Analysis, Notes 16: Hilbert function spaces (basics)

In the final week of the semester we will study **Hilbert function spaces** (also known as **reproducing kernel Hilbert spaces**) with the goal of presenting an operator theoretic proof of the classical Pick interpolation theorem. Since time is limited I will present a somewhat unorthodox route, and ignore much of the beautiful function theory involved. BGU students who wish to learn more about this should consider taking Daniel Alpay’s course next semester. Let me also note the helpful lecture notes available from Vern Paulsen’s webpage and also this monograph by Jim Agler and John McCarthy (in this post and the next one I will refer to these as [P] and [AM] below).

(Not directly related to this post, but might be of some interest to students: there is an amusing discussion connected to earlier material in the course (convergence of Fourier series) here).