Estimates for the modulus of smoothness
In approximation theory it is usual for the order of approximation of a function to be given in terms of the modulus of smoothness of that function, but in practice a quantitative estimate of this modulus will be required. In this paper we introduce certain classes of multivariate functions which are characterized by the singularities of their elements. For these classes we obtain sharp quantitative estimates of the modulus of smoothness of any order with respect to both the \(L_ q\) and uniform norms. The aim is to make the theoretical approximation results more accessible to the practical user.
scientific article; zbMATH DE number 3907059
scientific article