Zur \(L^ 2\) Bestapproximation eines konvexen Körpers durch einen bewegten konvexen Körper. (On the \(L^ 2\)-best approximation of a convex body by a moved convex body)

DOI10.1007/BF01501130zbMath0712.52005MaRDI QIDQ748887

Randolf Arnold

Publication date: 1989

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178449

zbMATH Keywords

convex bodyFourier seriesoptimal locationSteiner pointsEuclidean motionsdeciding theoremL\({}^ 2\)-best approximation

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Inequalities and extremum problems involving convexity in convex geometry (52A40) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (2)

Inner products for Convex Bodies ⋮ On the Sobolev distance of convex bodies

Cites Work

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• On the Brunn-Minkowski theorem
• Polygonal approximation of plane convex bodies
• A pre-Hilbert space consisting of classes of convex sets
• Krümmungsschwerpunkte konvexer Körper. II. (Barycenter of curvature of convex bodies. II)
• Approximation problems for convex polyhedra
• Metrics for sets of convex bodies
• The Steiner Point of a Convex Polytope

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