The limit of the zero set of polynomials of the Fibonacci type

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• 作者：Albrecht Bö ; ttcher^a ; ^{aboettch@mathematik.tu-chemnitz.de" class="auth_mail" title="E-mail the corresponding author} ; Fuad Kittaneh^b ; ^{fkitt@ju.edu.jo" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11B39 ; secondary ; 15A18 ; 15B05 ; 30C15 ; 47B35
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：163
• 期：Complete
• 页码：89-100
• 全文大小：812 K

文摘

The paper concerns the limit of the zero set S_n$S_n$ of the Fibonacci-type polynomials G_n(x)=G_n(a,b,x)$G_n(x)=G_n(a,b,x)$ given by 7b20e4f288eaa8cad" title="Click to view the MathML source">G₀(x)=a$G_0(x)=a$, G₁(x)=x+b$G_1(x)=x+b$, and G_n+2(x)=xG_n+1(x)+G_n(x)$G_{n+2}(x)=x{G}_{n+1}(x)+G_n(x)$. It presents an explicit set L   consisting of at most two points such that S_n$S_n$ converges to the union of [−2i,2i]$[-2i,2i]$ and L in the Hausdorff metric. The proof is based on the asymptotic analysis of the eigenvalues of special non-Hermitian perturbations of Hermitian Toeplitz matrices.