International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 9, Pages 517-534
doi:10.1155/S0161171201010936
Biorthogonal multiresolution analyses and decompositions of Sobolev spaces
Department of Mathematics, Faculty of Sciences of Tunis, Campus 1060, Tunis, Tunisia
Received 25 September 2000; Revised 1 February 2001
Copyright © 2001 Abdellatif Jouini and Khalifa Trimèche. 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.
Abstract
The object of this paper is to construct extension operators in
the Sobolev spaces Hk(]−∞,0]) and Hk([0,+∞[)(k≥0). Then we use these extensions to get biorthogonal
wavelet bases in Hk(ℝ). We also give a construction in L2([−1,1]) to see how to obtain boundaries functions.