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On Bounded Functions with Bounded nth Differences

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Hassler Whitney Collected Papers

Part of the book series: Contemporary Mathematicians ((CM))

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Abstract

We consider real valued functions f defined in a closed interval I (bounded or unbounded), with nth differences

$$ \Delta _{h}^{n}f(x) = \sum\limits_{i} {{{{( - 1)}}^{{n - i}}}} \left( {\begin{array}{*{20}{c}} n \\ i \\ \end{array} } \right)f(x + ih) $$

bounded for some fixed n.

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References

  1. J. C. Burkill,Polynomial approximations to functions with bounded differences,J. London Math. Soc. vol. 33 (1958) pp. 157–161.

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  2. F.John, 1958 (unpublished)

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  3. H. Whitney,Derivatives, difference quotients and Taylor’s formula,Bull. Amer. Math. Soc. vol. 40 (1934) pp. 89–94.

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  4. H. Whitney,On functions with bounded nth differences,J. Math. Pures Appl. (9) vol. 36 (1957) pp. 67–95.

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Authors
  1. Hassler Whitney
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Warwick, CV 4 7AL, Coventry, England

    James Eells

  2. Department of Mathematics, University of Utah, 84112, Salt Lake City, Utah, USA

    Domingo Toledo

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© 1992 Birkhäuser Boston

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Whitney, H. (1992). On Bounded Functions with Bounded nth Differences. In: Eells, J., Toledo, D. (eds) Hassler Whitney Collected Papers. Contemporary Mathematicians. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2972-8_30

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  • DOI: https://doi.org/10.1007/978-1-4612-2972-8_30

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7740-8

  • Online ISBN: 978-1-4612-2972-8

  • eBook Packages: Springer Book Archive

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