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CERTAIN CONDITIONS FOR MEAN CONVERGENCE OF HERMITE AND HERMITE-FEJER INTERPOLATION POLYNOMIALS WITH ERDOS-TYPE WEIGHTS
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Let Q ∈ C1(R) : R → [0, ∞) be an even function. We consider the exponential weight w(x) = exp(-Q(x)), x ∈ R. In this paper we obtain certain conditions for mean convergence theorems of the higher order Hermite- Fejer interpolation polynomials based at the zeros of the orthogonal polynomials with respect to the exponential weight.
Abstract
Let Q ∈ C1(R) : R → [0, ∞) be an even function. We consider the exponential weight w(x) = exp(-Q(x)), x ∈ R. In this paper we obtain certain conditions for mean convergence theorems of the higher order Hermite- Fejer interpolation polynomials based at the zeros of the orthogonal polynomials with respect to the exponential weight.
참고문헌 (11)
- Z. Damelin, "Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdos Weights II", Can. J. Math, 48, pp.737~757 (1996)
- H. S. Jung, "Orthonormal polynomials with exponential-type weights", J. Approx. Theory, 152, pp.215~238 (2008)
- 정희선, "Specific examples of exponential weights", 대한수학회논문집, 24(2), pp.303~319 (2009), 대한수학회
- H. S. Jung, "Markov-Bernstein inequality and Hermite-Fejer interpolation for exponential-type weights", J. Approx. Theory, 162, pp.1381~1397 (2010)
- H. S. Jung, "Derivatives of integrating functions for orthonormal polynomials with exponential-type weights", J. Inequalities and Applications, 2010, pp.29~ (2010)
- H. S. Jung, "Mean and uniform convergence of Lagrange interpolation with Erdos-type weights", JIA 2012, pp.237~ (2012)
- H. S. Jung, "Convergence or divergence of higher or-der Hermite or Hermite-Fejer interpolation polynomials with exponential-type weights", ISRN Mathematical Analysis, 2012, pp.31~ (2012)[DOI]
- H. S. Jung, "Lp-CONVERGENCE OF HIGHER ORDER HERMITE OR HERMITE-FEJÉR INTERPOLATION POLYNOMIALS WITH EXPONENTIAL-TYPE WEIGHTS", Advanced Studies in Contemporary Mathematics, 25(3), pp.317~333 (2015), 장전수학회
- A. L. Levin, "Orthogonal Polynomials for Exponential Weights" (2001), Springer
- D. S. Lubinsky, "A Survey of Weighted Polynomial Approximation with Exponential Weights", Surveys In Approximation Theory, 3, pp.1~105 (2007)
- R. Sakai, "Mollification of exponential weights and its application to the Markov-Bernstein inequality", Pioneer J. of Math., 7(1), pp.83~101 (2013)
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 제3호HERMITE 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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