Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in Lp

M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We consider γ-weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in a weighted Lp norm with 1≤p≤∞. The domain of the functions is Dd, where D⊆R is a bounded or unbounded interval. We provide conditions on the weights γ that guarantee that anchored and ANOVA spaces are equal (as sets of functions) and have equivalent norms with equivalence constants uniformly or polynomially bounded in d. Moreover, we discuss applications of these results to integration and approximation of functions on Dd.

Original languageEnglish
Pages (from-to)78-99
Number of pages22
JournalJournal of Complexity
Volume40
DOIs
StatePublished - Jun 1 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

  • ANOVA decomposition
  • Anchored decomposition
  • General weights
  • Sobolev spaces
  • Tractability of multivariate problems
  • Unbounded domains

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics (all)
  • Control and Optimization
  • Applied Mathematics

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