Abstract
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 biorthogonal 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.
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