Approximation in L ₂ by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator

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• 作者：D. V. Gorbachev ; V. I. Ivanov
• 关键词：Sturm–Liouville operator on the half ; line ; the space L2 ; Fourier transform ; Jackson’s inequality ; Gauss quadrature formula
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：100
• 期：3-4
• 页码：540-549
• 全文大小：684 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876
• 卷排序：100

文摘

For approximations in the space L₂(ℝ₊) by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator, we prove Jackson’s inequality with exact constant and optimal argument in the modulus of continuity. The optimality of the argument in the modulus of continuity is established using the Gauss quadrature formula on the half-line over the zeros of the eigenfunction of the Sturm–Liouville operator.