ON THE APPROXIMABILITY AND CURSE OF DIMENSIONALITY OF CERTAIN CLASSES OF HIGH-DIMENSIONAL FUNCTIONS\ast

In this paper, we study the approximability of high-dimensional functions that appear, for example, in the context of many body expansions and high-dimensional model representation. Such functions, though high-dimensional, can be represented as finite sums of lower-dimensional functions. We will derive sampling inequalities for such functions, give explicit advice on the location of good sampling points, and show that such functions do not suffer from the curse of dimensionality.