Speaker
Ilya Videnskii
(St. Petersburg State University)
Description
For a reproducing kernel Hilbert space $H$ on a set $X$ we define a distance $d(a,Z)$ between a point $a$ and a subset $Z$. A space $H$ has the Schwarz-Pick kernel if for every pair $(a,Z)$ there exists an extremal multiplier of norm less or equal than one, which vanishes at the set $Z$ and attains the value $d(a,Z)$ at the point $a$. For a normalized Hilbert space with Schwarz-Pick kernel and for a sequence of subsets that satisfies an abstract Blaschke condition we prove that the associate Blaschke product of extremal multipliers converges in the norm of $H$.
Primary author
Ilya Videnskii
(St. Petersburg State University)
