Weighted Polynomial Approximation on the Real Line
โ Scribed by A. Kroo; J. Szabados
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 635 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
โฆ Synopsis
We study polynomial approximation on the whole real line with weight (w=e^{-Q}), where (Q) has polynomial growth at infinity. The following are the main problems considered: asymptotics for the Markov factors and for the rate of best approximation of (|x|), Jackson-type estimates for the degree of best approximation of some classes of functions. 1995 Academic Press. Inc.
๐ SIMILAR VOLUMES
It is shown that if weighted polynomials w n P n with deg P n n converge uniformly on the support of the extremal measure associated with w, then they converge to 0 everywhere else. It is also shown that uniform approximation on the support can always be characterized by a closed subset Z having the
We obtain discrepancy theorems for the distribution of the zeros of extremal polynomials arising in the theory of weighted polynomial approximation on the whole real axis.