CONSTRUCTION OF SCHAUDER DECOMPOSITION ON BANACH-SPACES OF PERIODIC-FUNCTIONS

This paper deals with Schauder decompositions of Banach spaces X-2 pi of 2 pi-periodic functions by projection operators P-k onto the subspa ces V-k k = 0, 1,..., which form a multiresolution of X-2 pi. The resu lts unify the study of wavelet decompositions by orthogonal projection s in the Hilbert space L-2 pi(2) on one hand and by interpolatory proj ections in the Banach space C-2 pi on the other. The approach, using ' 'orthogonal splines'', is constructive and leads to the construction o f a Schauder decomposition of X-2 pi and a biorthogonal system for X-2 pi and its dual X-2 pi. Decomposition and reconstruction algorithms are derived from the construction.