Cyclicity in Dirichlet-type spaces and extremal polynomials

DOI10.1007/S11854-015-0017-1zbMath1320.30090arXiv1301.4375OpenAlexW1564066951MaRDI QIDQ2352248

Constanze Liaw, Daniel Seco, Alberto A. Condori, Catherine Bénéteau, Alan A. Sola

Publication date: 30 June 2015

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4375

zbMATH Keywords

Dirichlet-type spacecyclic functionoptimal approximant

Mathematics Subject Classification ID

Cyclic vectors, hypercyclic and chaotic operators (47A16) Hardy spaces (30H10) Bergman spaces and Fock spaces (30H20)

Related Items (18)

Equidistribution of zeros of some polynomials related to cyclic functions ⋮ Optimal polynomial approximants in \(L^p\) ⋮ Optimal approximants and orthogonal polynomials in several variables ⋮ Simultaneous zero-free approximation and universal optimal polynomial approximants ⋮ A note on cyclic vectors in Dirichlet-type spaces in the unit ball of ⋮ Some problems on optimal approximants ⋮ General Optimal Polynomial Approximants, Stabilization, and Projections of Unity ⋮ Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants ⋮ An optimal approximation problem for free polynomials ⋮ More properties of optimal polynomial approximants in Hardy spaces ⋮ Polynomial approach to cyclicity for weighted \(\ell^p_A\) ⋮ Cyclicity in reproducing kernel Hilbert spaces of analytic functions ⋮ Optimal approximants and orthogonal polynomials in several variables II: Families of polynomials in the unit ball ⋮ A note on Dirichlet-type spaces and cyclic vectors in the unit ball of \(\mathbb C^2\) ⋮ A survey of optimal polynomial approximants, applications to digital filter design, and related open problems ⋮ Boundary behavior of optimal polynomial approximants ⋮ Cyclic polynomials in two variables ⋮ Remarks on Inner Functions and Optimal Approximants

Cites Work

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• The Dirichlet space: a survey
• Invariant subspaces in Banach spaces of analytic functions
• Cyclicity in the Dirichlet space
• On the Brown-Shields conjecture for cyclicity in the Dirichlet space
• Zeros of cesàro sum approximations
• Cyclic Vectors in the Dirichlet Space
• Some Examples of Cyclic Vectors in the Dirichlet Space
• Invertible Elements in the Dirichlet Space

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