Some properties of classes of real self-reciprocal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Botta, Vanessa¹  Bracciali, Cleonice F.²  Pereira, Junior A.³ 

[1] UNESP Univ Estadual Paulista, FCT, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP, Brazil

[2] UNESP Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[3] UNESP Univ Estadual Paulista, FCT, Programa Posgrad Matemat Aplicada & Computac, BR-19060900 Presidente Prudente, SP, Brazil

关键词: Self-reciprocal polynomials;    Unit circle;    Zeros;    Monotonicity;    Interlacing;   

DOI  :  10.1016/j.jmaa.2015.08.038

来源: Elsevier

【 摘 要 】

The purpose of this paper is twofold. Firstly we investigate the distribution, simplicity and monotonicity of the zeros around the unit circle and real line of the real self-reciprocal polynomials R-n((lambda)) = 1+lambda(z + z(2) +...+ z(n-1)) +z(n), n >= 2 and lambda is an element of R. Secondly, as an application of the first results we give necessary and sufficient conditions to guarantee that all zeros of the self-reciprocal polynomials [GRAPHICS] [GRAPHICS] [GRAPHICS] given by Kim and Park in 2008. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free