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Converse and Smoothness Theorems for Erdős Weights inL_(0<p⩽∞)

✍ Scribed by S.B. Damelin

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 529 KB
Volume: 93
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3178

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✦ Synopsis

We prove converse and smoothness theorems of polynomial approximation in weighted L p spaces with norm & fW& L p (R) ( 0<p) for Erdo s weights on the real line. In particular we prove characterization theorems involving realization functionals and thereby establish some interesting properties of our weighted modulus of continuity.

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Jackson Theorems for Erdős Weigh

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✍ S.B. Damelin; D.S. Lubinsky 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 572 KB

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 the

Converse and Smoothness Theorems for Erdo&#x030B;s Weights inL_(0<p⩽∞)

✦ Synopsis

Converse and Smoothness Theorems for Erdős Weights inL_(0<p⩽∞)