Application of basic splines for sampling multidimensional signals of finite duration

We investigate limitations of sampling theory for signals with finite spect ra, which are particularly prone to appearance during measurements in multi dimensional spaces. We present a method for sampling with several arguments , using basic splines, Fourier transforms, and the Parseval equality. We pr esent an example of adaptive optimization of the sampling grid for a magnet ic field that is associated with a spectrum of multidimensional signals hav ing fractal similarity.