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Note on approximating complex zeros of a polynomial

โœ Scribed by Bernard Friedman


Publisher
John Wiley and Sons
Year
1949
Tongue
English
Weight
513 KB
Volume
2
Category
Article
ISSN
0010-3640

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๐Ÿ“œ SIMILAR VOLUMES


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โœ T.F. Xie; S.P. Zhou ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 161 KB

By establishing an identity for \(S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }_{j}^{n}\right) x^{j}(1-x)^{n-j}\), the present paper shows that a pointwise asymptotic estimate cannot hold for \(S_{n}(x)\), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic

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Let E be a subspace of C(X) and let R(E)= gร‚h: g, h # E ; h>0]. We make a simple, yet intriguing observation: if zero is a best approximation to f from E, then zero is a best approximation to f from R(E ). We also prove that if That extends the results of P. Borwein and S. Zhou who proved it for t

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It is shown that if weighted polynomials w n P n with deg P n n converge uniformly on the support of the extremal measure associated with w, then they converge to 0 everywhere else. It is also shown that uniform approximation on the support can always be characterized by a closed subset Z having the