Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
王国亮, 北京理工大学数学与统计学院
Inviter:
陈绍示
Title:
Root geometry of polynomials generated by a recursion of order two
Time & Venue:
2018.6.27 15:00-16:00 N202
Abstract:
We consider the root distribution of a sequence of univariate polynomials satisfying a recurrence of order two with linear polynomial coefficients. We show that the set of non-isolated limits of zeros of the polynomials is either an arc, or a circle, or a ``lollipop'', or an interval. As an application, we discover a sufficient and necessary condition for the universal real-rootedness of the polynomials, subject to certain sign condition on the coefficients of the recurrence.