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In this article, we analyze tensor approximation schemes for continuousfunctions. We assume that the function to be approximated lies in an isotropicSobolev space and discuss the cost when approximating this function in thecontinuous analogue of the Tucker tensor format or of the tensor train format.We especially show that the cost of both approximations are dimension-robustwhen the Sobolev space under consideration provides appropriate weights.

Analysis of tensor approximation schemes for continuous functions