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Forward and Converse Theorems of Polynomial Approximation for Exponential Weights on [−1, 1], II

✍ Scribed by D.S. Lubinsky

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
506 KB
Volume
91
Category
Article
ISSN
0021-9045

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✦ Synopsis

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 spaces with norm & fw& L p [&1, 1] for all 0<p , to match the forward theorems proved in part I of this paper.

1997 Academic Press

0<p

, where P n denote the polynomials of degree at most n. Our methods are similar to those in [8], where Jackson theorems were proved for Freud weights, and to the follow up papers [2,3] where Erdo s article no. AT963088 48

📜 SIMILAR VOLUMES

Forward and Converse Theorems of Polynom
Forward and Converse Theorems of Polynomial Approximation for Exponential Weights on [−1,&#xa0;1], I
✍ D.S. Lubinsky 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 522 KB

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,