A distance function on reproducing kernel Hilbert spaces. Lecture 2Лекция
Given H, a reproducing kernel Hilbert space of functions on X; the operator norm distance between reproducing kernels induces a metric on X. This metric arises naturally when quantifying properties of H, and in some cases determines H completely. I will give some background about this metric, discuss places where it is useful, and mention open questions. Specific subjects include interpolating sequences, the maximal ideal space of the multiplier algebra, and isometric embedding of X into hyperbolic balls.