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Chebyshev–Schoenberg Operators

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Abstract

We show that a given space of splines with sections in a given Extended Chebyshev space gives birth to infinitely many positive linear operators of Schoenberg-type. As a consequence of the properties of Chebyshevian B-spline bases such operators are automatically variation-diminishing. Among other results, we show that the set of two-dimensional spaces they reproduce is stable under knot insertion and dimension elevation, and we establish a simple sufficient condition for convergence.

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Authors and Affiliations

  1. Laboratoire Jean Kuntzmann, Université Joseph Fourier, BP53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

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  1. Marie-Laurence Mazure
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Correspondence to Marie-Laurence Mazure.

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Communicated by Tim N.T. Goodman.

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Mazure, ML. Chebyshev–Schoenberg Operators. Constr Approx 34, 181–208 (2011). https://doi.org/10.1007/s00365-010-9123-6

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  • DOI: https://doi.org/10.1007/s00365-010-9123-6

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