, Volume 34, Issue 3, pp 371-391
Date: 22 Dec 2010

Regularity of Tensor Product Approximations to Square Integrable Functions

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We investigate first-order conditions for canonical and optimal subspace (Tucker format) tensor product approximations to square integrable functions. They reveal that the best approximation and all of its factors have the same smoothness as the approximated function itself. This is not obvious, since the approximation is performed in L 2.

Communicated by: Wolfgang Dahmen.