On direct and converse theorems in the theory of weighted polynomial approximation
✍ Scribed by Géza Freud
- Publisher
- Springer-Verlag
- Year
- 1972
- Tongue
- French
- Weight
- 408 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0025-5874
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📜 SIMILAR VOLUMES
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.
We consider exponential weights of the form w :=e &Q on (&1, 1) where Q(x) is even and grows faster than (1&x 2 ) &$ near \1, some $>0. For example, we can take where exp k denotes the kth iterated exponential and exp 0 (x)=x. We prove Jackson theorems in weighted L p spaces with norm & fw& Lp(&1,
We consider exponential weights of the form w :=e &Q on [&1, 1] where Q(x) is even and grows faster than (1&x 2 ) &$ near \1, some $>0. For example, we can take where exp k denotes the kth iterated exponential and exp 0 (x)=x. We prove converse theorems of polynomial approximation in weighted L p s