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