\(\mathbb C\)-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation

DOI10.1155/IJMMS/2006/80846zbMath1135.46007MaRDI QIDQ885585

Lars Filipsson

Publication date: 14 June 2007

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/54023

zbMATH Keywords

convexity, \({\mathbb C}\)-convexity, Hahn-Banach Theorem, Mazur's Theorem, Kergin interpolation, holomorphic convexity

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) (Spaces of) multilinear mappings, polynomials (46G25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Cites Work

• A formula for Kergin interpolation in \(R^ k\).
• A natural interpolation of \(C^ k \)functions
• Complex Kergin interpolation
• Characterization of continuous selections of the metric projection for spline functions
• Complex convexity and analytic functionals
• Notions of convexity
• Best approximation in inner product spaces
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