© Hindawi Publishing Corp. BIORTHOGONAL MULTIRESOLUTION ANALYSES AND DECOMPOSITIONS OF SOBOLEV SPACES

Abstract

Abstract. The object of this paper is to construct extension operators in the Sobolev spaces H k (]−∞,0]) and H k ([0,+∞[) (k ≥ 0). Then we use these extensions to get biorthogonal wavelet bases in H k (R). We also give a construction in L 2 ([−1,1]) to see how to obtain boundaries functions. 2000 Mathematics Subject Classification. 41A58, 42C15