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<p>We obtain sharp inequalities for the best mean square approximation of two classes of functions on the half-line, defined by boundary conditions corresponding to even and odd extension of a function. Optimal subspaces are provided by even and odd parts of the spaces generated by equidistant shifts of a single function. Under certain additional conditions on this function, the sharpness of the inequalities in the sense of average widths is proved. Bibliography: 9 titles.</p>

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OPTIMAL SUBSPACES FOR MEAN SQUARE APPROXIMATION OF CLASSES OF DIFFERENTIABLE FUNCTIONS ON THE HALF-LINE

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • O. L. Vinogradov,
  • A. Yu. Ulitskaya

摘要

We obtain sharp inequalities for the best mean square approximation of two classes of functions on the half-line, defined by boundary conditions corresponding to even and odd extension of a function. Optimal subspaces are provided by even and odd parts of the spaces generated by equidistant shifts of a single function. Under certain additional conditions on this function, the sharpness of the inequalities in the sense of average widths is proved. Bibliography: 9 titles.