Piecewise continuous spline wavelets on irregular grid

Piecewise continuous spline of Lagrange type are constructed. An embedding of spline spaces is established for arbitrary refinement of grids. The system of biorthogonal linear functionals to splines is constructed. Wavelet decompositions and decomposition and reconstruction algorithms in the case of an infinite flow for a grid on an open interval and a finite flow for a grid on a segment are constructed.