Harmonic functions of maximal growth: invertibility and cyclicity in Bergman spaces

DOI10.1090/S0894-0347-97-00244-0zbMath0963.30033OpenAlexW1549285998MaRDI QIDQ4372635

Haakan Hedenmalm, Alexander Borichev

Publication date: 16 December 1997

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

Full work available at URL: https://doi.org/10.1090/s0894-0347-97-00244-0

zbMATH Keywords

Bergman spacescyclic vectorscanonical divisors

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Invariant subspaces of linear operators (47A15) Spaces of bounded analytic functions of one complex variable (30H05) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items

Weighted Bergman spaces: shift-invariant subspaces and input/state/output linear systems ⋮ Beurling's theorem for the Bergman space ⋮ Hilbert spaces of analytic functions with a contractive backward shift ⋮ Weighted integrability of polyharmonic functions ⋮ Cyclic vectors in Fock-type spaces in multi-variable case ⋮ Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants ⋮ The Newman-Shapiro problem ⋮ The dual of a Bergman space on simply connected domains. ⋮ Large Bergman spaces: Invertibility, cyclicity, and subspaces of arbitrary index. ⋮ Criterion of weak invertibility in weighted \(L^p\) spaces of entire Fock-type functions ⋮ Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space ⋮ An expansive multiplier property for operator-valued Bergman inner functions ⋮ A characterization of Dirichlet-inner functions ⋮ On polynomial approximation in anisotropic weighted spaces of holomorphic functions in a polydisc ⋮ Free outer functions in complete Pick spaces

Cites Work

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• Contractive zero-divisors in Bergman spaces
• An extension of the Nevanlinna theory
• A Beurling-type theorem
• Beurling type density theorems in the unit disk
• Linear and complex analysis problem book 3. Part 1
• Invariant subspaces in Bergman spaces and the biharmonic equation
• Beurling's theorem for the Bergman space
• Outer functions and cyclic elements in Bergman spaces
• On Absolutely Convergent Exponential Sums
• A factorization theorem for square area-integrable analytic functions.
• Cyclic Vectors in A -∞
• Weakly Invertible Elements in the Space of Square-Summable Holomorphic Functions

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