On the converse theorems of weighted polynomial approximation
โ Scribed by G. Freud
- Publisher
- Akadmiai Kiad
- Year
- 1973
- Tongue
- English
- Weight
- 348 KB
- Volume
- 24
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
๐ 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
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 degre