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An estimate of the width of a class of functions in the space \(L_ 2\). (Russian) Zbl 0776.41018

The author presents the following two assertions: \[ d_ n(W^ r_ \omega;L_ 2(\mathbb{R},e^{-x^ 2}))\asymp n^{r/2}\omega(n^{- 1/2})(n>r),d_ n(\tilde W^ r_ \omega;L_ 2[-1,+1])\asymp n^{- r}\omega(n^{-1}) (n>r); \] and proves the second one. For notations consult the reviewed paper.

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A30 Approximation by other special function classes
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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