The convergence of a sequence of polynomials with restricted zeros

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Kim, Min-Hee¹  Kim, Young-One^1,2  Lee, Jungseob³ 

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Ajou Univ, Dept Math, Suwon 16499, South Korea

关键词: Zeros of polynomials and entire functions;    Laguerre-Polya class;    Polya-Obrechkoff class;    Appell polynomials;    Jensen polynomials;   

DOI  :  10.1016/j.jmaa.2019.06.005

来源: Elsevier

【 摘 要 】

Suppose that (f(n)) is a sequence of polynomials,(f(n)((k))(0)) converges for every non negative integer k, and that the limit is not 0 for some k. It is shown that if all the zeros of f(1), f(2),. . . lie in the closed upper half plane Im z >= 0, or if f(1), f(2),... are real polynomials and the numbers of their non-real zeros are uniformly bounded, then the sequence converges uniformly on compact sets in the complex plane. The results imply a theorem of Benz and a conjecture of Polya. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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