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On multivariate approximation by continuous linear operators

Part of the Lecture Notes in Mathematics book series (LNM,volume 571)

Keywords

  • Tensor Product
  • Convergence Order
  • Bernstein Polynomial
  • Interpolation Operator
  • Cross Norm

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References

  1. BUTZER, P. L.: On two-dimensional Bernstein polynomials. Canadian J. Math. 5, 107–113 (1953).

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  6. HAUSSMANN, W., POTTINGER, P.: Zur Konvergenz mehrdimensionaler Interpolationsverfahren. Z. Angew. Math. Mech. 53, T195–T197 (1973).

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  7. HAUSSMANN, W., POTTINGER, P.: On the construction and convergence of multivariate interpolation operators. To appear in J. Approximation Theory.

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  8. NATANSON, I. P.: Constructive function theory, Vol. III. New York: Ungar 1965.

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  9. POTTINGER, P.: Zur linearen Approximation im Raum Ck(I). Habilitationsschrift. Duisburg 1976.

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  10. SCHATTEN, R.: A theory of cross spaces. Annals of Math. Studies No. 28. Princeton: Princeton University Press 1950.

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  11. SHISHA, O., MOND, B.: The rapidity of convergence of the Hermite-Fejér approximation to functions of one or several variables. Proc. Amer. Math. Soc. 16, 1269–1276 (1965).

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© 1977 Springer-Verlag Berlin · Heidelberg

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Haußmann, W., Pottinger, P. (1977). On multivariate approximation by continuous linear operators. In: Schempp, W., Zeller, K. (eds) Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086567

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  • DOI: https://doi.org/10.1007/BFb0086567

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08069-5

  • Online ISBN: 978-3-540-37496-1

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