Displaying similar documents to “B-spline bases and osculating flats: One result of H.-P. Seidel revisited”

Unconditionality of orthogonal spline systems in H¹

Gegham Gevorkyan, Anna Kamont, Karen Keryan, Markus Passenbrunner (2015)

Studia Mathematica

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We give a simple geometric characterization of knot sequences for which the corresponding orthonormal spline system of arbitrary order k is an unconditional basis in the atomic Hardy space H¹[0,1].

Spline functions and total positivity.

M. Gasca (1996)

Revista Matemática de la Universidad Complutense de Madrid

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In this survey we show the close connection between the theory of Spline Functions and that of Total Positivity. In the last section we mention some recent results on totally positive bases which are optimal for shape preserving properties in Computer Aided Geometric Design.

B-spline bases and osculating flats : one result of H.-P. Seidel revisited

Marie-Laurence Mazure (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Along with the classical requirements on B-splines bases (minimal support, positivity, normalization) we show that it is natural to introduce an additional “end point property”. When dealing with multiple knots, this additional property is exactly the appropriate requirement to obtain the poles of nondegenerate splines as intersections of osculating flats at consecutive knots.