Biorthogonal multiresolution analyses and decompositions of Sobolev spaces (Q1607772)

The object of this paper is to construct extension operators in the Sobolev spaces \(H^k(-\infty, 0]\) and \(H^k[0, \infty)\) (\(k \geq 0\)). These extensions are then used to get biorthogonal wavelet bases in \(H^k(R)\). The authors also construct a segmented multiresolution analysis in \(L^2[-1,1]\) to show more clearly how to obtain boundary functions.