Invariant Subspaces of the Dirichlet Shift and Pseudocontinuations

DOI10.2307/2154587zbMath0816.47037OpenAlexW4256574549MaRDI QIDQ4286814

C.-E. Sundberg, Stephan Richter

Publication date: 12 April 1994

Full work available at URL: https://doi.org/10.2307/2154587

zbMATH Keywords

extremal functionsinvariant subspacesDirichlet spaceDirichlet shiftpseudocontinuation to the exterior disc

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Spaces of bounded analytic functions of one complex variable (30H05) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Linear operators on function spaces (general) (47B38) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)

Related Items (17)

Cyclicity and invariant subspaces in Dirichlet spaces ⋮ Approximation of invariant subspaces in some Dirichlet-type spaces ⋮ Prolongations and cyclic vectors ⋮ Fine boundary behavior and invariant subspaces of harmonically weighted Dirichlet spaces ⋮ Havin-Mazya type uniqueness theorem for Dirichlet spaces ⋮ Harmonically weighted Dirichlet spaces associated with finitely atomic measures ⋮ Extremal functions and invariant subspaces in Dirichlet spaces ⋮ Local Dirichlet spaces as de Branges-Rovnyak spaces ⋮ Cyclicity in Dirichlet type spaces ⋮ On the index of invariant subspaces in the space of weak products of Dirichlet functions ⋮ The jumping operator on invariant subspaces in spaces of analytic functions ⋮ Cyclicity in the Dirichlet space ⋮ The backward shift on the space of Cauchy transforms ⋮ Regularity for generators of invariant subspaces of the Dirichlet shift ⋮ On the Brown-Shields conjecture for cyclicity in the Dirichlet space ⋮ Invariant subspaces and Nevanlinna-Pick kernels ⋮ Free outer functions in complete Pick spaces

Cites Work

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• Cyclic Vectors in the Dirichlet Space
• Invariant subspaces of the Dirichlet shift.
• Invariant Subspaces in Banach Spaces of Analytic Functions
• A Representation Theorem for Cyclic Analytic Two-Isometries
• Solution of the Problem of Plateau

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