The multidimensional Jackson theorem in \(L_ p\)
The approximation of \(2\pi\)-periodic functions in several variables is investigated by trigonometric polynomials from the so-called hyperbolic cross. This means roughly, that one can only use trigonometric polynomials which contain only terms with the property that the product of the frequencies (in each variable) is bounded by a number \(n\), and the question is the behavior of this best approximant when \(n\to\infty\) (recall, that in the classical case the \textit{sum} of the frequences is bounded by \(n)\). In the paper under review the author gives an estimate for the best \(L_ p\)-approximation by trigonometric polynomials from the hyperbolic cross. The exact definitions are too involved to be recorded here.
approximation of \(2\pi\)-periodic functions in several variables
scientific article; zbMATH DE number 148620