Regularity of Tensor Product Approximations to Square Integrable Functions
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- Uschmajew, A. Constr Approx (2011) 34: 371. doi:10.1007/s00365-010-9125-4
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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 L2.