Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials
Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher order extended Hermite-Fejér interpolation op...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/542653 |
| Summary: | Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher order extended Hermite-Fejér interpolation operator based on the zeros of . When is even, we show that Lebesgue constants of these interpolation operators are and , respectively; that is, and . In the case of the Hermite-Fejér interpolation polynomials for , we can prove the weighted uniform convergence. In addition, when is odd, we will show that these interpolations diverge for a certain continuous function on , proving that Lebesgue constants of these interpolation operators are similar or greater than log . |
|---|---|
| ISSN: | 1110-757X 1687-0042 |