Regularity of Tensor Product Approximations to Square Integrable Functions

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Approximation rates for the hierarchical tensor format in periodic Sobolev spaces (2014, background): “In [49] it is shown that for best approximations g ∈ C≤r of f ∈ Bs ⊃ Bs,mix the factors uμk also have Sobolev regularity s, and therefore might be nicely approximable.”
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Die Darstellung ist alles andere als erschöpfend, sondern orientiert sich lose an den im Literaturverzeichnis gelisteten Arbeiten des Autors.”
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “The results in [146, 27] show in particular that the lower-dimensional component functions in L2–best approximations of given rank can be approximated at precisely the rates that are approached by our explicit construction of H1–approximations, which in each case correspond to three times the rate o”