Constructive Approximation

, Volume 24, Issue 1, pp 49–70

Best N Term Approximation Spaces for Tensor Product Wavelet Bases

  • Pal-Andrej Nitsche
Article

DOI: 10.1007/s00365-005-0609-6

Cite this article as:
Nitsche, PA. Constr Approx (2006) 24: 49. doi:10.1007/s00365-005-0609-6

Abstract

We consider best N term approximation using anisotropic tensor product wavelet bases ("sparse grids"). We introduce a tensor product structure ⊗q on certain quasi-Banach spaces. We prove that the approximation spaces Aαq(L2) and Aαq(H1) equal tensor products of Besov spaces Bαq(Lq), e.g., Aαq(L2([0,1]d)) = Bαq(Lq([0,1])) ⊗q · ⊗q Bαq · ·(Lq([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales of Besov spaces.

Best N term approximationTensor product approximationSparse gridsBesov spaces

Copyright information

© Springer 2006

Authors and Affiliations

  • Pal-Andrej Nitsche
    • 1
  1. 1.Seminar for Applied Mathematics, ETH-Zentrum, CH-8092 ZurichSwitzerland