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Innocent Ndikubwayo: Criterion of reality of zeros in a polynomial sequence satisfying a three-term recurrence relation

Time: Fri 2019-03-01 13.00 - 14.00

Location: Room 22, building 5, Kräftriket, Department of Mathematics, Stockholm University

Lecturer: Speaker: Innocent Ndikubwayo

Abstract: In this talk we establish the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence {Pi } generated by a three-term recurrence relation \(P_i (x) + Q_1 (x)P_{i−1} (x) + Q_2 (x)P_{i-2}(x) = 0\) with the standard initial conditions \(P_0(x) = 1, P_{-1} (x) = 0\), where \(Q_1(x)\) and \(Q_2(x)\) are arbitrary real polynomials.