Beschreibung:
Abstract A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the 𝑠-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial, but by the Euclidean degree, defined in terms of the 2-norm rather than the 1-norm of the exponent vector 𝗄 of a monomial x 1 k 1 ⋯ x s k s .