Skip to main content
Log in

Best N Term Approximation Spaces for Tensor Product Wavelet Bases

  • Published:
Constructive Approximation Aims and scope

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 Aα q(L2) and Aα q(H1) equal tensor products of Besov spaces Bα q(Lq), e.g., Aα q(L2([0,1]d)) = Bα q(Lq([0,1])) ⊗q · ⊗q Bα q · ·(Lq([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales of Besov spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nitsche, PA. Best N Term Approximation Spaces for Tensor Product Wavelet Bases. Constr Approx 24, 49–70 (2006). https://doi.org/10.1007/s00365-005-0609-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00365-005-0609-6

Navigation