Toral algebraic sets and function theory on polydisks Authors
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 in ℂ n whose intersection with T n is 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 14J70 32A65 Key Words and Phrases Toral variety inner function H ∞ Pick interpolation
Communicated by John Erik Fornæss
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