Biorthogonal multiresolution analyses and decompositions of Sobolev spaces

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.