On Wavelet Decompositionof Spaces Of First Order Splines

摘要

We consider approximate relations in the form of a system of linear algebraic equations that yield B_φ-splines. We construct Lagrange type splines of the first order and give examples of polynomial, trigonometric, hyperbolic, and exponential B_φ-splines. We also construct a system of linear functionals biorthog-onal to the B_φ-splines and resolve an interpolation problem generated by this system. For refined nonuniform grids we establish an embedding of spaces of B_φ-splines. The decomposition and reconstruction formulas are obtained. Bibliography: 20 titles.