Geometry of uniqueness varieties for a three-point Pick problem in $\mathbb{D}^3$

Abstract

Motivated by the recent progress of research on extending holomorphic functions defined on subvarieties of classical domains and its connections to the 3-point Pick interpolation, we study a special class of twodimensional algebraic subvarieties Mα of the unit tridisc, defined as the sets

Determining sets for holomorphic functions on the symmetrized bidisk

“…Here, the distinguished boundary of a bounded domain Ω ⊂ C d is the Šilov boundary with respect to the algebra of complex-valued functions continuous on Ω and holomorphic in Ω. A special type of algebraic varieties has been prevalent in the study of uniqueness of the solutions of a Pick interpolation problem (see [6,[22][23][24][25]27]). We define it below.…”