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Total Positivity of the Spline Kernel and its Applications

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Total Positivity and Its Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 359))

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Abstract

We discuss here some results from Approximation Theory which are based on the total positivity of the truncated power function (x - t) r-1+ . A detailed study of the B-splines with Birkhoff’s knots is presented. Results on monosplines of minimal norm and their relation to optimal quadrature formulas are reviewed. A historical note concerning a paper of Tschakaloff from 1938 on B-splines is included.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Sofia, Blvd. James Boucher 5, 1126, Sofia, Bulgaria

    Borislav Bojanov

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  1. Borislav Bojanov
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Editors and Affiliations

  1. Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain

    Mariano Gasca

  2. IBM, T.J. Watson Research Center, Yorktown Heights, New York, USA

    Charles A. Micchelli

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© 1996 Springer Science+Business Media Dordrecht

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Bojanov, B. (1996). Total Positivity of the Spline Kernel and its Applications. In: Gasca, M., Micchelli, C.A. (eds) Total Positivity and Its Applications. Mathematics and Its Applications, vol 359. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8674-0_1

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  • DOI: https://doi.org/10.1007/978-94-015-8674-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4667-3

  • Online ISBN: 978-94-015-8674-0

  • eBook Packages: Springer Book Archive

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