Abstract
We consider weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in L1 or L∞ norms. We provide conditions on the weights under which the corresponding spaces have equivalent norms with constants independent of, or only polynomially dependent on the number of variables.
| Original language | English |
|---|---|
| Pages (from-to) | 1-19 |
| Number of pages | 19 |
| Journal | Journal of Complexity |
| Volume | 32 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 1 2016 |
Bibliographical note
Publisher Copyright:© 2015 Elsevier Inc.
Funding
We thank Michael Gnewuch for valuable comments and Henryk Woźniakowski for suggesting to consider polynomial equivalence. Significant part of the paper has been written at Institute for Computational and Experimental Research in Mathematics , Brown University, where the authors participated at the Semester Program on “High-dimensional Approximation”, Fall 2014. We thank the Staff of the Institute for great hospitality. Finally we thank the anonymous referees for valuable comments.
| Funders | Funder number |
|---|---|
| Institute for Computational and Experimental Research in Mathematics | |
| Brown University |
Keywords
- ANOVA decomposition
- Anchored decomposition
- Embeddings
- Equivalence of norms
- Tractability
- Weighted function spaces
ASJC Scopus subject areas
- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- General Mathematics
- Control and Optimization
- Applied Mathematics