Dimension elevation in Müntz spaces: a new emergence of the Müntz condition

DOI10.1016/j.jat.2014.01.006zbMath1288.65017arXiv1309.0938OpenAlexW2092591406MaRDI QIDQ2441941

Rachid Ait-Haddou

Publication date: 31 March 2014

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

Full work available at URL: https://arxiv.org/abs/1309.0938

zbMATH Keywords

algorithmconvergenceSchur functionsChebyshev blossomingdimension elevationMüntz spacesChebyshev-Bernstein basesChebyshev-Bézier curvesGelfond-Bernstein bases

Mathematics Subject Classification ID

Approximation by operators (in particular, by integral operators) (41A35) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (8)

Approximation by Chebyshevian Bernstein operators versus convergence of dimension elevation ⋮ Control point based exact description of curves and surfaces, in extended Chebyshev spaces ⋮ Constructing totally positive piecewise Chebyshevian B-spline bases ⋮ Sparse Pythagorean hodograph curves ⋮ Interpolation of \(G^1\) Hermite data by \(C^1\) cubic-like sparse Pythagorean hodograph splines ⋮ Approximation by Müntz spaces on positive intervals ⋮ The Hyers-Ulam stability constant for Chebyshevian Bernstein operators ⋮ Nested sequences of rational spaces: Bernstein approximation, dimension elevation, and Pólya-type theorems on positive polynomials

Cites Work

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• Geometry of Müntz spaces and related questions
• On Chebyshevian spline subdivision
• Cutting corners always works
• Blossoming: A geometrical approach
• Chebyshev-Bernstein bases
• Convergence of subdivision and degree elevation
• Gelfond-Bézier curves
• A Müntz type theorem for a family of corner cutting schemes
• Chebyshev blossoming in Müntz spaces: toward shaping with Young diagrams
• Muntz type Theorems I
• Inverse scattering with fixed energy and an inverse eigenvalue problem on the half-line
• A Generalization of a Theorem of Bôcher

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