대한수학회지 (Journal of the Korean Mathematical Society)

  • 제45권1호
  • /
  • Pages.177-196
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  • 2008
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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HERMITE AND HERMITE-FEJÉR INTERPOLATION OF HIGHER ORDER AND ASSOCIATED PRODUCT INTEGRATION FOR ERDÖS WEIGHTS

  • Jung, Hee-Sun (Department of Mathematics Education Sungkyunkwan University)
  • 발행 : 2008.01.31
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초록

Using the results on the coefficients of Hermite-Fej$\acute{e}$r interpolations in [5], we investigate convergence of Hermite and Hermite-$Fej{\acute{e}}r$ interpolation of order m, m=1,2,... in $L_p(0<p<{\infty})$ and associated product quadrature rules for a class of fast decaying even $Erd{\H{o}}s$ weights on the real line.

키워드

참고문헌

  1. S. B. Damelin and D. S. Lubinsky, Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Erdos weights I, Can. J. Math. 48 (1996), no. 4, 710-736 https://doi.org/10.4153/CJM-1996-037-1
  2. Z. Ditzian and V. Totik, Moduli of Smoothness, Springer Series in Computational Mathematics, 9, Springer-Verlag, Berlin, 1987
  3. G. Freud, Orthogonal polynomials, Pergamon Press, Oxford, 1971
  4. H. S. Jung, $L_{\infty}$ convergence of interpolation and Associated Product integration for exponential weights, J. Approx. Theory 120 (2003), no. 2, 217-241 https://doi.org/10.1016/S0021-9045(02)00020-5
  5. H. S. Jung, On coefficients of Hermite-Fejer interpolations, Arch. Inequal. Appl. 1 (2003), no. 1, 91-109
  6. A. L. Levin, D. S. Lubinsky, and T. Z. Mthembu, Christoffel functions and orthogonal polynomials for Erdos weights on ($-{\infty},{\infty}$), Rend. Mat. Appl. 14 (1994), no. 7, 199-289
  7. D. S. Lubinsky, The weighted $L_{p}$-norms of orthogonal polynomials for Erdos weights, Comput. Math. Appl. 33 (1997), 151-163 https://doi.org/10.1016/S0898-1221(96)00227-1
  8. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, Heidelberg, 1997

피인용 문헌

  1. On the dense divergence of the product quadrature formulas of interpolatory type vol.433, pp.2, 2016, https://doi.org/10.1016/j.jmaa.2015.08.056