Biorthogonal systems of functionals and decomposition matrices for minimal splines

摘要

For the minimal splines of arbitrary order on a nonuniform grid, a system of linear functionals biorthogonal to the system of coordinate splines is constructed. The matrices of refining and sparsing decompositions are obtained for the spaces of splines of arbitrary order associated with infinite and finite nonuniform grids on an interval and on a segment, respectively.