Optimal quadrature problem on <Emphasis Type="Italic">n</Emphasis>-information for Hardy-Sobolev classes |
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Authors: | Xue Hua Li Gen Sun Fang |
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Institution: | [1]College of Science, China Agricultural University, Beijing 100083, P. R. China [2]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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Abstract: | For β > 0 and an integer r ≥ 2, denote by (H)\tilde]¥,br\tilde H_{\infty ,\beta }^r those 2π-periodic, real-valued functions f on ℝ, which are analytic in S
β
:= {z ∈ ℂ: |Im z| < β} and satisfy the restriction |f
(r)(z)|≤1, z ∈ S
β
. The optimal quadrature formulae about information composed of the values of a function and its kth (k = 1, ..., r − 1) derivatives on free knots for the classes (H)\tilde]¥,br\tilde H_{\infty ,\beta }^r are obtained, and the error estimates of the optimal quadrature formulae are exactly determined. |
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Keywords: | Hardy-Sobolev class analytic function optimal quadrature formula n-information |
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