de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem

DOI10.1016/j.aim.2020.107315OpenAlexW3046597166MaRDI QIDQ2196622

Daniel Alpay, Victor Vinnikov, Ariel Pinhas

Publication date: 3 September 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.08670

zbMATH Keywords

compact Riemann surfaceBeurling-Lax theoremde Branges Rovnyak spacesoperator vesselsjoint transfer function

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (4)

Reflection positivity via Krein space analysis ⋮ Beurling-Lax type theorems and Cuntz relations ⋮ Commuting operators over Pontryagin spaces with applications to system theory ⋮ Flexibility of analysis serving computational polynomial algebra or arithmetics

Cites Work

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• Determinantal representations of singular hypersurfaces in \(\mathbb P^n\)
• Dilations of semigroups of contractions through vessels
• Elementary transformations of determinantal representations of algebraic curves
• Complete description of determinantal representations of smooth irreducible curves
• Cayley-Hamilton theorem, vector bundles and divisors of commuting operators
• The Pick interpolation theorem for finitely connected domains
• Models for noncontractions
• A class of subnormal operators related to multiply-connected domains
• Invariant subspaces on open Riemann surfaces. II
• Operator waves in Hilbert space and related partial differential equations
• Self-adjoint determinantal representations of real plane curves
• Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
• Finite dimensional de Branges spaces on Riemann surfaces
• Representations of Lie algebras by non-skewselfadjoint operators in Hilbert space
• Livsic-type determinantal representations and hyperbolicity
• On a new class of structured reproducing kernel spaces
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Theta functions on Riemann surfaces
• Invariant subspaces on open Riemann surfaces
• Indefinite Hardy spaces on finite bordered Riemann surfaces
• Beurling-Lax type theorems in the complex and quaternionic setting
• Hall-order differentials on Riemann surfaces
• Bounded holomorphic functions and projections
• Sonine spaces of entire functions
• A joint spectrum for several commuting operators
• \({\mathcal H}^p\) sections of vector bundles over Riemann surfaces
• Zero-pole interpolation for meromorphic matrix functions on an algebraic curve and transfer functions of 2D systems
• Bounded analytic functions
• Open Riemann surfaces and extremal problems on compact subregions
• Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann
• LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future
• Meromorphic matrix trivializations of factors of automorphy over a Riemann surface
• Shifts on Hilbert spaces.
• Invariant subspaces of Hardy classes on infinitely connected open surfaces
• Zero-pole interpolation for matrix meromorphic functions on a compact Riemann surface and a matrix Fay trisecant identity
• Real fibered morphisms and Ulrich sheaves
• The 𝐻^{𝑝} spaces of an annulus
• Invariant Subspaces on Riemann Surfaces
• Ideals and Invariant Subspaces of Analytic Functions
• Inner and Outer Functions on Riemann Surfaces
• Invariant Subspace Theorems for Finite Riemann Surfaces
• Invariant subspaces of Hardy classes on infinitely connected plane domains
• Some Hilbert Spaces of Analytic Functions
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura

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