Complex mean-value interpolation and approximation of holomorphic functions

DOI10.1006/jath.1996.3096zbMath0904.32012OpenAlexW1987737888MaRDI QIDQ1375386

Lars Filipsson

Publication date: 26 January 1999

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1996.3096

zbMATH Keywords

convergence theoremsmean-value interpolationapproximation of holomorphic functionsformula of Hermite

Mathematics Subject Classification ID

Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30)

Related Items

Mikael Passare, a Jaunt in Approximation Theory ⋮ On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk ⋮ On the smoothness of certain composite functions ⋮ Interpolation spaces for PDE-preserving projectors on Hilbert-Schmidt entire functions ⋮ The Newton product of polynomial projectors Part 1: Construction and algebraic properties ⋮ Kergin interpolation in Banach spaces ⋮ Lagrange approximation in Banach spaces

Cites Work

• Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type
• Interpolation in minimum semi-norm and multivariate B-splines
• Divided differences, hyperbolic equations, and lifting distributions
• A shortcut to weighted representation formulas for holomorphic functions
• Multivariate interpolation and the Radon transform
• A formula for Kergin interpolation in \(R^ k\).
• A constructive approach to Kergin interpolation in \(R^ k\): Multivariate B-splines and Lagrange interpolation
• Kergin interpolation of entire functions on \(C^ n\).
• A natural interpolation of \(C^ k \)functions
• Complex Kergin interpolation
• On bounding spline interpolation
• Integral error formulae for the scale of mean value interpolations which includes Kergin and Hakopian interpolation
• Kergin interpolants of holomorphic functions
• Complex Kergin interpolation and the Fantappiè transform
• Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform
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