Cyclic Vectors in the Dirichlet Space

DOI10.2307/1999483zbMath0517.30040OpenAlexW4254191250MaRDI QIDQ3665414

Leon Brown, Allen L. Shields

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999483

zbMATH Keywords

invariant subspaceHadamard gapslogarithmic capacityDirichlet integralweak invertibility

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Banach spaces of continuous, differentiable or analytic functions (46E15)

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Cites Work

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• A representation formula for the Dirichlet integral
• Tangential boundary behavior of functions in Dirichlet-type spaces
• Multipliers of the Dirichlet space
• An analogue of a Hardy-Littlewood-Fejer inequality for upper triangular trace class operators
• Mergelyan sets and the modulus of continuity of analytic functions
• Approximation in the mean by polynomials on non-Caratheodory domains
• Weakly invertible elements in certain function spaces, and generators in \(l_ 1\)
• Subordinate \(H^ P\) functions
• Monotonic singular functions of high smoothness
• A subcollection of algebras in a collection of Banach spaces
• A density theorem for operator algebras
• Ensembles exceptionnels
• On two problems concerning linear transformations in Hilbert space
• Sets of uniqueness for functions regular in the unit circle
• On Nevanlinna's second theorem and extensions
• Cyclic elements in some spaces of analytic functions
• Weakly Invertible Elements in the Space of Square-Summable Holomorphic Functions
• Multipliers on D α
• The Structure of Monotone Functions
• Capacity of Sets and Fourier Series

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