Stable regions of Turan expressions

JOURNAL OF APPROXIMATION THEORY

卷:192

Article

Chasse, Matthew¹  Grabarek, Lukasz²  Visontai, Mirko¹ 

[1] Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

[2] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA

关键词: Hurwitz stability;    Orthogonal polynomials;    Turan inequalities;    Laguerre inequalities;   

DOI  :  10.1016/j.jat.2014.12.002

来源: Elsevier

【 摘 要 】

Consider polynomial sequences that satisfy a first-order differential recurrence. We prove that if the recurrence is of a special form, then the Turk expressions for the sequence are weakly Hurwitz stable (non-zero in the open right half-plane). A special case of our theorem settles a problem proposed by S. Fisk that the Turan expressions for the univariate Bell polynomials are weakly Hurwitz stable. We obtain related results for Chebyshev and Hermite polynomials, and propose several extensions involving Laguerre polynomials, Bessel polynomials, and Jensen polynomials associated to a class of real entire functions. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free