Abilov, A. A. An estimate of the width of a class of functions in the space \(L_ 2\). (Russian) Zbl 0776.41018 Mat. Zametki 52, No. 1, 3-8 (1992). 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. Reviewer: L.Leindler (Szeged) Cited in 1 ReviewCited in 3 Documents 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.) PDFBibTeX XMLCite \textit{A. A. Abilov}, Mat. Zametki 52, No. 1, 3--8 (1992; Zbl 0776.41018)