A NOTE ON THE BOUND OF WAVELET INTERPOLATION AND APPROXIMATION IN A BESOV SPACE

Linyuan Li (USA) and Yimin Xiao (USA)

Received January 13, 2009

References:

[1] A. Cohen, I. Daubechies and P. Vial, Wavelets on the interval and fast wavelet transforms, Appl. Comput. Harm. Anal. 1 (1993), 54-82. [2] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992. [3] D. L. Donoho and I. M. Johnstone, Minimax estimation via wavelet shrinkage, Ann. Statist. 26 (1998), 879-921. [4] Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, 1992. [5] C. E. Shannon, Communications in the presence of noise, Proc. I.R.E. 37 (1949), 10?21. [6] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992. [7] S. Zhang and M. Wong, Wavelet threshold estimation for additive regression models, Ann. Statist. 31 (2003), 152-173. [8] S. Zhang, M. Wong and Z. Zheng, Wavelet threshold estimation of a regression function with random design, J. Multivariate Anal. 80 (2002), 256-284.

Keywords and phrases: dyadic interpolation, function approximation, approximation errors, wavelets, Besov space.