Multidimensional B-spline forms and their Fourier transforms

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. This method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables.