We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction has been used in an exemplary way for guiding dimension- and scale-adaptive algorithms in application areas such as statistical learning theory, reduced order modeling, and information-based complexity. We prove results on compact embeddings, norm equivalences, and the estimation of   ϵ     ϵ       -dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.
['Michael Griebel', 'Peter Oswald']
Stable splittings of Hilbert spaces of functions of infinitely many variables