Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773818 | Journal of Complexity | 2017 | 36 Pages |
Abstract
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-dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Michael Griebel, Peter Oswald,