Rational approximation in the real Hardy space \(H_ 2\) and Stieltjes integrals: A uniqueness theorem

DOI10.1007/BF01229333zbMath0769.30024OpenAlexW2913775692MaRDI QIDQ1205133

Franck Wielonsky, Laurent Baratchart

Publication date: 1 April 1993

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01229333

zbMATH Keywords

uniqueness of best approximationStieltjes functionsrational approximation in \(H_ 2\)

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Approximation by rational functions (41A20)

Related Items (13)

An \(L^{p}\) analog to AAK theory for \(p\geq 2\) ⋮ A criterion for uniqueness of a critical point in \(H_ 2\) rational approximation ⋮ \(H^{\infty}\) interpolation and embedding theorems for rational functions ⋮ Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space ⋮ Application of a Bernstein type inequality to rational interpolation in the Dirichlet space ⋮ Cyclic AFD algorithm for the best rational approximation ⋮ Rational approximation in the real Hardy space \(H_ 2\) and Stieltjes integrals: A uniqueness theorem ⋮ Asymptotic error for \(L^2\) best rational approximants to Markov functions ⋮ Interpolation with constraints on the finite sets of the disc ⋮ Homogenization of Poisson's kernel and applications to boundary control ⋮ Zero distributions via orthogonality. ⋮ Piecewise rational approximation to continuous functions with characteristic singularities ⋮ Non-uniqueness of rational best approximants

Cites Work

• Identification and rational \(L^ 2\) approximation: A gradient algorithm
• Generalized monosplines and optimal approximation
• On the uniqueness of generalized monosplines of least \(L_ p\)-norm
• Index of critical points in rational \(\ell\) 2-approximation
• Rational approximation in the real Hardy space \(H_ 2\) and Stieltjes integrals: A uniqueness theorem
• Realization of systems with internal passivity and symmetry constraints
• On the uniqueness of monosplines and perfect splines of least L//1- and L//2-norm
• On the existence of optimal integration formulas for analytic functions
• Existence and Generic Properties of L² Approximants for Linear Systems
• On a class of best nonlinear approximation problems
• Properties of Minimal Integration Rules. II
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