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Lp-CONVERGENCE OF HIGHER ORDER HERMITE OR HERMITE-FEJÉR INTERPOLATION POLYNOMIALS WITH EXPONENTIAL-TYPE WEIGHTS

H. S. Jung|R. Sakai
장전수학회 (Jangjeon Mathematical Society)|2015.07|Advanced Studies in Contemporary Mathematics|제25권 제3호|pp. 317-333

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참고문헌

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초록

Let R = (-, ∞), and let Q ∈ C1(R) : R → R+ = [0, ∞) be an even function, which is an exponent. We consider the weight wρ(x) = |x|ρe-Q(x), ρ > 0, x ∈ R, and then we can construct the orthonormal polynomials pn(w2ρ; x) of degree n for w2ρ(x). In this paper we obtain Lp-convergence theorems of even order Hermite-Fejer interpolation polynomials at the zeros {xk,n,ρ}n k=1 of pn(w2 ρ; x).

Abstract

Let R = (-, ∞), and let Q ∈ C1(R) : R → R+ = [0, ∞) be an even function, which is an exponent. We consider the weight wρ(x) = |x|ρe-Q(x), ρ > 0, x ∈ R, and then we can construct the orthonormal polynomials pn(w2ρ; x) of degree n for w2ρ(x). In this paper we obtain Lp-convergence theorems of even order Hermite-Fejér interpolation polynomials at the zeros {xk,n,ρ}n k=1 of pn(w2 ρ; x).

참고문헌 (24)

  1. H. S. Jung, "Inequalities with exponential weights", JCAM, 212, pp.359~373 (2008)
  2. H. S. Jung, "Orthonormal polynomials with exponential-type weights", J. Approx. Theory, 152, pp.215~238 (2008)
  3. H. S. Jung, "Markov-Bernstein inequality and Hermite-Fejer interpolation for exponential-type weights", J. Approx. Theory, 162, pp.1381~1397 (2010)
  4. H. S. Jung, "Derivatives of integrating functions for orthonormal polynomials with exponential-type weights", J. Inequalities and Applications, 2009(528454), pp.22~ (2009)
  5. H. S. Jung, "Derivatives of orthonormal polynomials and coe±cients of Hermite-Fejer interpolation polynomial with exponential-type weights", J. Inequalities and Applications, 2010(816363), pp.29~ (2010)
  6. 정희선, "Specific examples of exponential weights", 대한수학회논문집, 24(2), pp.303~319 (2009), 대한수학회
  7. H. S. Jung, "Convergence or divergence of higher order Hermite or Hermite-Fejer interpolation polynomials with exponential-type weights", ISRN Mathematical Analysis, 2012(904169), pp.31~ (2012)[DOI]
  8. T. Kasuga, "Uniform or Mean Convergence of Hermite-Fejer Interpolation of Higher Order for Freud Weights", J. Approx. Theory, 101, pp.330~358 (1999)
  9. T. Kasuga, "Orthonormal polynomials with generalized Freud-type weights", J. Approx. Theory, 121, pp.13~53 (2003)
  10. T. Kasuga, "Orthonormal Polynomials for Generalized Freud-type Weights and Higher Order Hermite-Fejer Interpolation Polynomials", J. Approx. Theory, 127, pp.1~38 (2003)
  11. T. Kasuga, "Orthonormal polynomials for Laguerre-type weights", Far East J. Math. Sci. (FJMS), 15(1), pp.95~105 (2004)
  12. T. Kasuga, "Conditions for Uniform or Mean Convergence Hermite-Fej¶er Interpolation of Higher Order for Generalized Freud Weights", FJMS, 19, pp.145~199 (2005)
  13. Y. Kanjin, "Pointwise convergence of Hermite-Fejer interpolation of higher order for Freud weights", Tohoku Math. J, 46, pp.181~206 (1994)
  14. Y. Kanjin, "Convergence of the Derivatives of Hermite-Fejer Interpolation of Higher Order Based at the Zeros of Freud Polynomials Weights", J. Approx. Theory, 80, pp.378~389 (1995)
  15. D. S. Lubinsky, "Hermite-Fejer interpolation and associated product integration rules on the real line:The L1 Theory", J. Approx. Theory, 70, pp.284~334 (1992)
  16. A. L. Levin, "Orthogonal Polynomials for Exponential Weights" (2001), Springer
  17. R. Sakai, "Hermite-Fejer interpolation", Collo. Math. Soci. Janos Bolyai "Approx. Theory", pp.591~601 (1990)
  18. R. Sakai, "The degree of approximation of di®erentiable by Hermite interpolation polynomials", Acta Math. Acad. Sci. Hungar., 58, pp.11~ (1991)
  19. R. Sakai, "Progress in Approximation Theory", pp.731~759 (1991), Academic Press, Inc.
  20. R. Sakai, "Certain bounded Hermite-Fejer interpolation polynomials operator", Acta Math. Acad. Sci. Hungar, 59, pp.111~114 (1992)
  21. R. Sakai, "Hermite-Fejer interpolation of higher order III", Studia Sci. Math. Hungarica, 28, pp.87~97 (1993)
  22. R. Sakai, "Hermite-Fejer interpolation of higher order IV", Studia Sci. Math. Hungarica, 28, pp.379~386 (1993)
  23. R. Sakai, "Farvard-type theorem and Jackson-type theorem", Pioneer J. Math, 3(1), pp.1~16 (2011)
  24. R. Sakai, "Molli¯cation of exponential weights and its application to the Markov-Bernstein inequality", Pioneer J. Math, 7(1), pp.83~101 (2013)

관련 논문AI추천

CERTAIN 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 제4호HERMITE AND HERMITE-FEJER INTERPOLATION OF HIGHER ORDER AND ASSOCIATED PRODUCT INTEGRATION FOR ERDOS WEIGHTS정희선대한수학회 · 대한수학회지2008 · 제45권 제1호Radau quadrature for a rational almost quasi-Hermite-Fej{\'e}r-type interpolationLaxmi Rathour, Neha Mathur, Pankaj Mathur, Shrawan Kumar, Vishnu Narayan Mishra강원경기수학회 · 한국수학논문집2022 · 제30권 제1호Generalized Christoffel functions정해원강원경기수학회 · 한국수학논문집2010 · 제18권 제2호FULL QUADRATURE SUMS FOR GENERALIZED POLYNOMIALS WITH FREUD WEIGHTS정해원대한수학회 · 대한수학회논문집2010 · 제25권 제2호Specific examples of exponential weights정희선, Ryozi Sakai대한수학회 · 대한수학회논문집2009 · 제24권 제2호

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