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HERMITE AND HERMITE-FEJER INTERPOLATION OF HIGHER ORDER AND ASSOCIATED PRODUCT INTEGRATION FOR ERDOS WEIGHTS

정희선
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회지 (Journal of the KMS)|제45권 제1호|pp. 177-196

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참고문헌

키워드

Hermite and Hermite-Fejer interpolationsproduct integration rulesErdos weights.
주제분류수학

초록

Using the results on the coefficients of Hermite-Fej´er interpolations in [5], we investigate convergence of Hermite and Hermite-Fej´er interpolation of order m, m = 1, 2,... in Lp(0 < p < ∞) and associated product quadrature rules for a class of fast decaying even Erd˝os weights on the real line.

Abstract

Using the results on the coefficients of Hermite-Fej´er interpolations in [5], we investigate convergence of Hermite and Hermite-Fej´er interpolation of order m, m = 1, 2,... in Lp(0 < p < ∞) and associated product quadrature rules for a class of fast decaying even Erd˝os weights on the real line.

참고문헌 (8)

  1. S. B. Damelin, "Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Erdos weights I", Canadian Journal of Mathematics, 48(4), pp.710~736 (1996)
  2. Z. Ditzian, "Moduli of Smoothness, Springer Series in Computational Mathematics", pp.9~ (1987), Springer-Verlag
  3. G. Freud, "Orthogonal polynomials" (1971), Pergamon Press
  4. H. S. Jung, "L1 convergence of interpolation and Associated Product integration for exponential weights", Journal of Approximation Theory, 120(2), pp.217~241 (2003)
  5. H. S. Jung, "On coefficients of Hermite-Fejer interpolations", Archives of Inequalities and Applications, 1(1), pp.91~109 (2003)
  6. A. L. Levin, "Christoffel functions and orthogonal polynomials for Erdos weights on (¡1;1)", Rendiconti di Matematica e delle sue Applicazioni, 14(7), pp.199~289 (1994)
  7. D. S. Lubinsky, "The weighted Lp-norms of orthogonal polynomials for Erdos weights", Computers & Mathematics with Applications, 33, pp.151~163 (1997)
  8. E. B. Saff, "Logarithmic Potentials with External Fields" (1997), Springer-Verlag

관련 논문AI추천

Lp-CONVERGENCE OF HIGHER ORDER HERMITE OR HERMITE-FEJÉR INTERPOLATION POLYNOMIALS WITH EXPONENTIAL-TYPE WEIGHTSH. S. Jung, R. Sakai장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제3호CERTAIN CONDITIONS FOR MEAN CONVERGENCE OF HERMITE AND HERMITE-FEJER INTERPOLATION POLYNOMIALS WITH ERDOS-TYPE WEIGHTS정희선, RYOZI SAKAI장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호Radau quadrature for a rational almost quasi-Hermite-Fej{\'e}r-type interpolationLaxmi Rathour, Neha Mathur, Pankaj Mathur, Shrawan Kumar, Vishnu Narayan Mishra강원경기수학회 · 한국수학논문집2022 · 제30권 제1호FULL QUADRATURE SUMS FOR GENERALIZED POLYNOMIALS WITH FREUD WEIGHTS정해원대한수학회 · 대한수학회논문집2010 · 제25권 제2호Hermite-type exponentially fitted interpolation formulas using three unequally spaced nodes김경중대한수학회 · 대한수학회논문집2022 · 제37권 제1호Generalized Christoffel functions정해원강원경기수학회 · 한국수학논문집2010 · 제18권 제2호

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