Distinguished varieties through the Berger-Coburn-Lebow theorem

DOI10.2140/apde.2022.15.477OpenAlexW2996782568WikidataQ113727186 ScholiaQ113727186MaRDI QIDQ2128855

Poornendu Kumar, Tirthankar Bhattacharyya, Haripada Sau

Publication date: 22 April 2022

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.01410

zbMATH Keywords

algebraic varietiesjoint spectruminner functionsdistinguished varietiescommuting isometrieslinear pencils

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Linear operator methods in interpolation, moment and extension problems (47A57) Dilations, extensions, compressions of linear operators (47A20) Analytic subsets and submanifolds (32C25) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items (3)

Essentially normal quotient weighted Bergman modules over the bidisk and distinguished varieties ⋮ Determining sets for holomorphic functions on the symmetrized bidisk ⋮ Pure inner functions, distinguished varieties and toral algebraic commutative contractive pairs

Cites Work

• Unnamed Item
• Unnamed Item
• Nevanlinna-Pick interpolation on distinguished varieties in the bidisk
• Dilations of \(\varGamma\)-contractions by solving operator equations
• Ando dilations, von Neumann inequality, and distinguished varieties
• Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc
• Representation and index theory for \(C^*\)-algebras generated by commuting isometries
• Rational dilation problems associated with constrained algebras
• Factorizations of contractions
• Algebraic and geometric aspects of rational \(\Gamma\)-inner functions
• Analytic Toeplitz operators, distinguished varieties and boundary behavior of symbols
• Inner functions on the bidisk and associated Hilbert spaces
• Function theory on the Neil parabola
• Distinguished varieties
• Spectral sets and distinguished varieties in the symmetrized bidisc
• A joint spectrum for several commuting operators
• Dilations and constrained algebras
• Subvarieties of the tetrablock and von Neumann\'s inequality
• Polynomials defining distinguished varieties
• Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc
• Maximum theorems for vector valued holomorphic functions

This page was built for publication: Distinguished varieties through the Berger-Coburn-Lebow theorem