This paper is concerned with multivariate analogues of
many standard results in the L∞-approximation theory of functions of one real variable, cf. [12], [13], [14], [20], [21] and [24]. In particular, asymptotic bounds are given for the distance of a given smooth function from various finite-dimensional spaces such as multivariate trigonometric polynomials, multivariate algebraic polynomials and multivariate polynomial spline functions
