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Sharp Nikolskii inequalities with exponential weights

✍ Scribed by P. Nevai; V. Totik


Book ID
112650997
Publisher
Springer
Year
1987
Tongue
English
Weight
274 KB
Volume
13
Category
Article
ISSN
0133-3852

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Inequalities with exponential weights
✍ H.S. Jung; R. Sakai 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 205 KB

Let R = (-∞, ∞) and let Q ∈ C 2 : R → R + = [0, ∞) be an even function. Then in this paper we consider the infinite-finite range inequality, an estimate for the Christoffel function, and the Markov-Bernstein inequality with the exponential weights w (x)= |x| e -Q(x) , x ∈ R.

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Let \(W:=e^{-Q}\) where \(Q\) is even, sufficiently smooth, and of faster than polynomial growth at infinity. Such a function \(W\) is often called an Erdös weight. In this paper we prove Nikolskii inequalities for Erdös weights. We also motivate the usefulness of, and prove a Bernstein inequality o