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

✍ Scribed by D.S. Lubinsky

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
522 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 Jackson theorems in weighted L p spaces with norm & fw& Lp(&1, 1) for all 0<p . In part II of this paper, we shall prove matching converse theorems. 1997 Academic Press &( f&P) w& Lp(&1, 1) , (1.2) 0<p

, where P n denote the polynomials of degree at most n.

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Forward and Converse Theorems of Polynom
Forward and Converse Theorems of Polynomial Approximation for Exponential Weights on [−1,&#xa0;1], II
✍ D.S. Lubinsky 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 506 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 converse theorems of polynomial approximation in weighted L p s