Spline wavelets on the unit circle
Spline function spaces over refined partitions form an excellent setting for multiresolution analysis which in turn leads to wavelet construction. The author considers complex spline function spaces defined on the unit circle with equispaced nodes and obtains an orthonormal basis in terms of the B-splines [cf. \textit{M. Kamada}, \textit{K. Toraichi} and \textit{R. Mori}, J. Approximation Theory 55, No. 1, 27-34 (1988; Zbl 0679.41007)]. Two scale equations for such orthonormal bases are also derived. Thus a decomposition of the space of square integrable functions over \([0,2\pi]\) into different orthogonal subspaces is obtained. The decomposition and reconstruction formulas each consist of only two terms.
scientific article; zbMATH DE number 1029207