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Jackson Theorems for Erdős Weights inLp(0<p⩽∞)

✍ Scribed by S.B. Damelin; D.S. Lubinsky

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 572 KB
Volume: 94
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1998.3199

No coin nor oath required. For personal study only.

✦ Synopsis

An Erdo s weight is of the form W :=e &Q where Q is even and of faster than polynomial growth at . For example, we can take

where exp k denotes the kth iterated exponential. We prove Jackson theorems in weighted L p spaces with norm & fW& L p (R) for all 0<p . These are the first proper Jackson theorems for Erdo s weights even in L . An interesting feature is a Timan Nikolskii Brudnyi effect: The degree of approximation improves towards the endpoints of a certain interval. By contrast, there is no such feature for Freud weights.

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Jackson Theorems for Erdo&#x030B;s Weights inLp(0<p⩽∞)

✦ Synopsis

Jackson Theorems for Erdős Weights inLp(0<p⩽∞)