1987
DOI: 10.1070/im1987v028n01abeh000870
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Approximation of Periodic Functions of Several Variables by Bilinear Forms

Abstract: Differential crms sections are calculated for the electron impact excitation of 1%-2's transitions in helium at incident energies of 100 and 200eV. A distorted wave approximation b used with the effect of target polarization taken into acmunt. The results are compared with the recent experimental data of Sakai e r d and with the recent R-matrix method calculation of Nakazaki er al. The present cross section is in general agreement with the R-matrix calculation. It is found, however, that the present calculatio… Show more

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Cited by 15 publications
(42 citation statements)
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“…This is due to the almost the same approximation properties between these two classes, more details see [28]. On the other hand, for dominated mixed smoothness class which is traditionally considered in multivariate approximation and integration.…”
Section: Statement Of Resultsmentioning
confidence: 94%
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“…This is due to the almost the same approximation properties between these two classes, more details see [28]. On the other hand, for dominated mixed smoothness class which is traditionally considered in multivariate approximation and integration.…”
Section: Statement Of Resultsmentioning
confidence: 94%
“…X n is linear subspace of L ∞ (I d ) with dimension n. Based on (4.1) and the known results about Kolmogorov n-width on anisotropic classes [28], we see that for the integration problem of F r p (I d ), 1 p < 2, we can find an exponent which satisfies the requirement of tractability for ε −1 . As mentioned in section 2, the tractability problem is open even when r = ∞ and Novak provided a intractable results for positive quadrature formula.…”
mentioning
confidence: 88%
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“…We concentrate here on the papers published by Babaev (see [4]) and Temlyakov (see for example [26][27][28]). They were concerned with the following question: What is the exact asymptotic behavior of the quantities…”
Section: Explicit Estimatesmentioning
confidence: 99%
“…In a number of papers (see, for example, [2,3]), Temlyakov found the orders of the approximation TMr(F)v of classes of periodic functions of several variables by bilinear forms for d = l -d in F (u, v). These are the classes W vq,a , SW;,a , HVq, and YH~ of periodic functions that are defined by restrictions on the corresponding partial derivatives or prelimit differences.…”
Section: Theorem Let 2 I/q -D/p Then the Following Relation Is Valmentioning
confidence: 99%