DOI QR코드

DOI QR Code

SPECIFIC EXAMPLES OF EXPONENTIAL WEIGHTS

  • Published : 2009.04.30

Abstract

Let $Q\;{\in}\;C^2$ : ${\mathbb{R}}\;{\rightarrow}\;[0,{\infty})$ be an even function. Then we will consider the exponential weights w(x) = exp(-Q(x)) in the weight class from [2]. In the paper, we will give some relations among exponential weights in this class and introduce a new weight subclass. In addition, we will investigate some properties of the typical and specific weights in these weight classes.

References

  1. Y. Kanjin and R. Sakai, Pointwise convergence of Hermite-Fejer interpolation of higher order for Freud weights, Tohoku. Math. 46 (1994), 181–206 https://doi.org/10.2748/tmj/1178225757
  2. A. L. Levin and D. S. Lubinsky, Orthogonal Polynomials for Exponential Weights, Springer, New York, 2001
  3. P. Vertesi, Hermite-Fejer interpolations of higher order. I, Acta Math. Hungar. 54(1989), 135–152 https://doi.org/10.1007/BF01950715

Cited by

  1. Interpolation Polynomials of Entire Functions for Erdös-Type Weights vol.2013, 2013, https://doi.org/10.1155/2013/467351
  2. Positive Interpolation Operators with Exponential-Type Weights vol.2013, 2013, https://doi.org/10.1155/2013/421328
  3. On the Favard-Type Theorem and the Jackson-Type Theorem (II) vol.2011, 2011, https://doi.org/10.5402/2011/725638
  4. Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights vol.2012, 2012, https://doi.org/10.5402/2012/904169
  5. The de la Vallée Poussin Mean and Polynomial Approximation for Exponential Weight vol.2015, 2015, https://doi.org/10.1155/2015/706930
  6. Higher order Hermite-Fejér interpolation polynomials with Laguerre-type weights vol.2011, pp.1, 2011, https://doi.org/10.1186/1029-242X-2011-122
  7. Some Properties of Orthogonal Polynomials for Laguerre-Type Weights vol.2011, pp.1, 2011, https://doi.org/10.1155/2011/372874
  8. Mean and uniform convergence of Lagrange interpolation with the Erdős-type weights vol.2012, pp.1, 2012, https://doi.org/10.1186/1029-242X-2012-237
  9. A Study of Weighted Polynomial Approximations with Several Variables (I) vol.08, pp.09, 2017, https://doi.org/10.4236/am.2017.89095
  10. An estimate for derivative of the de la Vallée Poussin mean vol.47, pp.0, 2015, https://doi.org/10.5036/mjiu.47.1
  11. A Study of Weighted Polynomial Approximations with Several Variables (II) vol.08, pp.09, 2017, https://doi.org/10.4236/am.2017.89093
  12. Derivatives of Orthonormal Polynomials and Coefficients of Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights vol.2010, 2010, https://doi.org/10.1155/2010/816363
  13. Higher order derivatives of approximation polynomials on R $\mathbb{R}$ vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0789-y