Distinguished varieties
Copyright policy )Distinguished varieties
A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Ando's inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety, not the whole bidisk. We show that uniqueness sets for extremal Pick problems on the bidisk always contain a distinguished variety.
- University of Mary Washington United States
- University of California, San Diego United States
- University of Mary United States
isomorphism classes of distinguished varieties, biholomorphic bijection, Mathematics - Complex Variables, Analytic subsets and submanifolds, extension, Moduli, classification: analytic theory; relations with modular forms, inner functions, Functional Analysis (math.FA), Mathematics - Functional Analysis, Ando's inequality, admissible kernel, FOS: Mathematics, 47A20, Complex Variables (math.CV), analytic matrix-valued functions, Pick problem
isomorphism classes of distinguished varieties, biholomorphic bijection, Mathematics - Complex Variables, Analytic subsets and submanifolds, extension, Moduli, classification: analytic theory; relations with modular forms, inner functions, Functional Analysis (math.FA), Mathematics - Functional Analysis, Ando's inequality, admissible kernel, FOS: Mathematics, 47A20, Complex Variables (math.CV), analytic matrix-valued functions, Pick problem
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