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

Abdellatif Jouini and Khalifa Trimèche

 Department of Mathematics, Faculty of Sciences of Tunis, Campus 1060, Tunis, Tunisia
Received 25 September 2000; Revised 1 February 2001

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.