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Approximation by Polynomials with Restricted Zeros

✍ Scribed by J.G. Clunie; A.B.J. Kuijlaars

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
477 KB
Volume
79
Category
Article
ISSN
0021-9045

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✦ Synopsis

This paper discusses convergence properties of polynomials whose zeros lie on the real axis or in the upper half-plane. A result of Levin shows that uniform convergence of such polynomials to a non-zero limit on a complex sequence converging not too fast to a limit in the lower half-plane implies locally uniform convergence in C. We give a relatively simple proof of this result and present several extensions and examples which show that the criterion in Levin's theorem is almost sharp. 1994 Academic Press, Inc.

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