Interpolating sequences

After reviewing some basic facts on reproducing kernel Hilbert spaces, we see how they are applied to the study of interpolating sequences for bounded analytic functions. In particular, we see how the pseudo-hyperbolic geometry of the unit disk is entangled with the Euclidean geometry of the Hardy space: the separation of points in the disk corresponds to the separation of the related Szegő kernels. Time permitting, we see how such a correspondence extends to the bidisk.

Further reading: Agler–McCarthy, Pick Interpolation and Hilbert Function Spaces (AMS, 2002); Nikolski, Operators, Functions, and Systems: An Easy Reading, Vol. 2 (AMS, 2002); Garnett, Bounded Analytic Functions (Springer, 2007).