On some generalization of box splines

Zygmunt Wronicz

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 3, page 261-271
  • ISSN: 0066-2216

Abstract

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We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.

How to cite

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Wronicz, Zygmunt. "On some generalization of box splines." Annales Polonici Mathematici 72.3 (1999): 261-271. <http://eudml.org/doc/262844>.

@article{Wronicz1999,
abstract = {We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.},
author = {Wronicz, Zygmunt},
journal = {Annales Polonici Mathematici},
keywords = {approximation; Chebyshevian splines; box splines; interpolation},
language = {eng},
number = {3},
pages = {261-271},
title = {On some generalization of box splines},
url = {http://eudml.org/doc/262844},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Wronicz, Zygmunt
TI - On some generalization of box splines
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 3
SP - 261
EP - 271
AB - We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
LA - eng
KW - approximation; Chebyshevian splines; box splines; interpolation
UR - http://eudml.org/doc/262844
ER -

References

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  1. [1] B. D. Bojanov, H. A. Hakopian, and A. A. Sahakian, Spline Functions and Multivariate Interpolations, Kluwer, 1993. Zbl0772.41011
  2. [2] C. de Boor and R. De Vore, Approximation by smooth multivariate splines, Trans. Amer Math. Soc. 276 (1983), 775-788. Zbl0529.41010
  3. [3] C. de Boor and K. Höllig, B-splines from parallelepipeds, J. Anal. Math. 42 (1982/83), 99-115. Zbl0534.41007
  4. [4] C. de Boor, K. Höllig, and S. Riemenschneider, Box Splines, Springer, 1993. Zbl0814.41012
  5. [5] C. de Boor, R. De Vore, and A. Ron, On the construction of multivariate (pre)wavelets, Constr. Approx. 9(1993), 123-166. Zbl0773.41013
  6. [6] K. Dziedziul, Box Splines, Wyd. P.G., Gdańsk, 1997 (in Polish). 
  7. [7] G. Fix and G. Strang, A Fourier analysis of the finite element variational method, in: Constructive Aspects of Functional Analysis, G. Geymonat (ed.), Cremonese, Rome, 1973, 793-840. 
  8. [8] K. Jetter, Multivariate approximation from the cardinal interpolation point of view, in: Approximation Theory VII (Austin, TX, 1992), E. W. Cheney, C. K. Chui, and L. L. Schumaker (eds.), Academic Press, 1993, 131-161. Zbl0767.41005
  9. [9] S. Karlin and W. J. Studden, Tchebysheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966. Zbl0153.38902
  10. [10] J. K. Kowalski, Application of box splines to the approximation of Sobolev spaces, J. Approx. Theory 61 (1990), 55-73. Zbl0709.41007
  11. [11] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971. Zbl0232.42007
  12. [12] Z. Wronicz, Chebyshevian splines, Dissertationes Math. 305 (1990). 
  13. [13] Z. Wronicz, On some generalization of box splines, Preprint 34 (January 97), Instytut Matematyki AGH. Zbl0959.41009
  14. [14] Z. Wronicz, On some properties of box splines, Preprint 25 (January 98), Wydział Matematyki Stosowanej AGH. Zbl0959.41009

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