Minimally supported error representations and approximation by the constants
In this paper the author constructs minimally supported Peano kernel type representations for linear functionals such as the error in multivariate Hermite interpolation. The case of representing the error in approximation to \(f\) by the constant polynomial \(f(a)\) in terms of integrals of the first order derivatives of \(f\) is discussed in detail. It is shown that there exist many representations, which are not minimally supported and involve the integration of first order derivatives over multidimensional regions. Using the representations for the error discussed here the distance of smooth functions from the constants in the uniform norm is estimated.
scientific article; zbMATH DE number 1484806
scientific article