On the best approximation of functions of many variables by algebraic polynomials
The author considers problems concerning the approximation of non-periodic functions of \(N\) variables by algebraic polynomials. For this purpose he introduces the notation of \(k\)-th difference that characterizes the smoothness of functions of \(N\) variables. Utilizing this he proves several interesting theorems pertaining to the relations between the structural properties of non-periodic functions of \(N\) variables and their best approximation by algebraic polynomials.
scientific article; zbMATH DE number 982580