The Journal of Geometric Analysis

, Volume 16, Issue 4, pp 551–562

Toral algebraic sets and function theory on polydisks

Authors

  • Jim Agler
    • U.C. San Diego
  • John E. McCarthy
    • Washington University
  • Mark Stankus
    • California Polytechnic State University
Article

DOI: 10.1007/BF02922130

Cite this article as:
Agler, J., McCarthy, J.E. & Stankus, M. J Geom Anal (2006) 16: 551. doi:10.1007/BF02922130

Abstract

A toral algebraic set A is an algebraic set innwhose intersection with Tnis sufficiently large to determine the holomorphic functions on A. We develop the theory of these sets, and give a number of applications to function theory in several variables and operator theoretic model theory. In particular, we show that the uniqueness set for an extremal Pick problem on the bidisk is a toral algebraic set, that rational inner functions have zero sets whose irreducible components are not toral, and that the model theory for a commuting pair of contractions with finite defect lives naturally on a toral algebraic set.

Math Subject Classifications

14J7032A65

Key Words and Phrases

Toral varietyinner functionHPick interpolation

Copyright information

© Mathematica Josephina, Inc. 2006