Geodesic
Lower bounds for separable approximations of the Hilbert kernel
Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 425-432

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Asymptotically best possible lower bounds for separable approximations are obtained for the function $1/(x+y)$. The method used for the derivation of such bounds is based on the generalization of the maximal volume principle for low-rank approximations. Bibliography: 10 titles. 
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     author = {I. V. Oseledets},
     title = {Lower bounds for separable approximations of the {Hilbert} kernel},
     journal = {Sbornik. Mathematics},
     pages = {425--432},
     publisher = {mathdoc},
     volume = {198},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_3_a4/}
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I. V. Oseledets. Lower bounds for separable approximations of the Hilbert kernel. Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 425-432. http://geodesic.mathdoc.fr/item/SM_2007_198_3_a4/