The failure of rational dilation on a triply connected domain

DOI10.1090/S0894-0347-05-00491-1zbMath1089.47009arXivmath/0310398OpenAlexW1676154571MaRDI QIDQ5313363

Michael A. Dritschel, Scott A. McCullough

Publication date: 29 August 2005

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310398

zbMATH Keywords

transfer functiontheta functiondilationRiemann surfacespectral setinner functionmultiply connected domainHerglotz representationNevanlinna-Pick interpolationFay reproducing kernel

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Dilations, extensions, compressions of linear operators (47A20) Moment problems and interpolation problems in the complex plane (30E05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spectral sets of linear operators (47A25) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Kernel functions in one complex variable and applications (30C40)

Related Items (19)

Contractions and the Commutant Lifting Theorem in Kreĭn Spaces ⋮ An Introduction to Hilbert Module Approach to Multivariable Operator Theory ⋮ Rational dilation problems associated with constrained algebras ⋮ Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting ⋮ Dilations and constrained algebras ⋮ Dilation theory and functional models for tetrablock contractions ⋮ Dilations of \(\varGamma\)-contractions by solving operator equations ⋮ Agler-commutant lifting on an annulus ⋮ Dilation theory: a guided tour ⋮ Interpolation in semigroupoid algebras ⋮ Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc ⋮ The von Neumann inequality for 3 × 3 matrices ⋮ Spectral sets and distinguished varieties in the symmetrized bidisc ⋮ The failure of rational dilation on the tetrablock ⋮ Survey of last ten years of work done in India in some selected areas of functional analysis and operator theory ⋮ Dilation theory in finite dimensions and matrix convexity ⋮ Test functions in constrained interpolation ⋮ Rational dilation of tetrablock contractions revisited ⋮ Tests for complete \(K\)-spectral sets

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