Мultidimensional functions' Approximation

It is proposed to represent a continuous function of several variables as a weighted sum of univariate functions, defined on a generalized basis, formed as a linear superposition of arguments of the assumed function. The approach under consideration is adapted to an optimum detecting filter structure and is used as a basis for a spline-filtering theory, developed by the authors. It can be used to solve a problem of signals reception on the background of noises and clutters, described by nonlinear stochastic differential equations. This scope of the problems will be covered in details in the following papers.