Biorthogonal multiresolution analyses and decompositions of Sobolev spaces
Abdellatif Jouini, Khalifa Trimèche · International Journal of Mathematics and Mathematical Sciences · 2001
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.