International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 9, Pages 517-534

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

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.


The object of this paper is to construct extension operators in the Sobolev spaces Hk(],0]) and Hk([0,+[)(k0). Then we use these extensions to get biorthogonal wavelet bases in Hk(). We also give a construction in L2([1,1]) to see how to obtain boundaries functions.