Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants

DOI10.1112/jlms/jdw057zbMath1356.42017arXiv1509.04807OpenAlexW3104396773MaRDI QIDQ2958286

Dmitry Khavinson, Alan A. Sola, Catherine Bénéteau, Constanze Liaw, Daniel Seco

Publication date: 1 February 2017

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

Full work available at URL: https://arxiv.org/abs/1509.04807

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items (15)

Optimal polynomial approximants in \(L^p\) ⋮ Optimal approximants and orthogonal polynomials in several variables ⋮ Simultaneous zero-free approximation and universal optimal polynomial approximants ⋮ Zeros of optimal polynomial approximants in \(\ell_A^p\) ⋮ On the prediction of \(p\)-stationary processes ⋮ Some problems on optimal approximants ⋮ Inner functions in weighted Hardy spaces ⋮ General Optimal Polynomial Approximants, Stabilization, and Projections of Unity ⋮ Analogues of finite Blaschke products as inner functions ⋮ Optimal approximants and orthogonal polynomials in several variables II: Families of polynomials in the unit ball ⋮ Quaternionic inner and outer functions ⋮ A survey of optimal polynomial approximants, applications to digital filter design, and related open problems ⋮ Boundary behavior of optimal polynomial approximants ⋮ Remarks on Inner Functions and Optimal Approximants ⋮ On the concept of inner function in Hardy and Bergman spaces in multiply connected domains

Cites Work

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• Cyclicity in reproducing kernel Hilbert spaces of analytic functions
• Coefficient estimates on weighted Bergman spaces
• Restriction operators, balayage and doubly orthogonal systems of analytic functions
• Zeros of extremal functions in weighted Bergman spaces.
• Extremal functions in invariant subspaces of Bergman spaces
• Weighted reproducing kernels and the Bergman space
• Cyclicity in Dirichlet-type spaces and extremal polynomials
• Fast algorithms for Toeplitz and Hankel matrices
• Canonical divisors in weighted Bergman spaces
• On the failure of optimal factorization for certain weighted bergman spaces
• Harmonic functions of maximal growth: invertibility and cyclicity in Bergman spaces

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