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The Scientific World Journal
Volume 2014 (2014), Article ID 102062, 16 pages
http://dx.doi.org/10.1155/2014/102062
Research Article

Approximation of Bivariate Functions via Smooth Extensions

College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China

Received 10 December 2013; Accepted 26 December 2013; Published 10 February 2014

Academic Editors: N. I. Mahmudov and S. Wang

Copyright © 2014 Zhihua Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications on Pure and Applied Mathematics, vol. 41, pp. 909–996, 1998. View at Google Scholar
  2. I. Daubechies, Ten Lectures on Wavelets, vol. 6 of CBMS-Conference Lecture Notes, SIAM, Philadelphia, Pa, USA, 1992.
  3. C. K. Chui, L. L. Schumaker, and J. Stockler, Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, 2002.
  4. C. K. Chui, W. Schempp, and K. Zeller, Multivariate Approximation Theory, Birkhauser, 1989.
  5. C. K. Chui, “Approximation induced by a fourier series,” Rocky Mountain Journal of Mathematics, vol. 4, no. 4, pp. 643–648, 1974. View at Google Scholar
  6. R. Long, Multidimensional Wavelet Analysis, International Publishing, Beijing, China, 1995.
  7. G. G. Lorentz, Approximation of Functions, Holt, Rinebart and Winston, 1966.
  8. P. Petrushev, “Multivariate n-term rational and piecewise polynomial approximation,” Journal of Approximation Theory, vol. 121, no. 1, pp. 158–197, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.
  10. A. F. Timan, Theory at Approximation of Functions of a Real Variable, Pergamon, 1963.
  11. Z. Zhang, “Convergence and Gibbs phenomenon of periodic wavelet frame series,” Rocky Mountain Journal of Mathematics, vol. 39, no. 4, pp. 1373–1396, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Zhang, “Measures, densities and diameters of frequency bands of scaling functions and wavelets,” Journal of Approximation Theory, vol. 148, no. 2, pp. 128–147, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. D. Zhou and K. Jetter, “Approximation with polynomial kernels and SVM classifiers,” Advances in Computational Mathematics, vol. 25, no. 1–3, pp. 323–344, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Zygmund, Trigonometric Series, I, II, Cambridge University Press, 2nd edition, 1968.