caa a22 4500 38636043X CHVBK 20180307111913.0 cr unu---uuuuu 161130e198912 xx s 000 0 eng 10.1017/S0004972700017433 doi S0004972700017433 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700017433 Jahangiri Massoud Department of Mathematica University of California Davis CA 95616 United States of America Weighted convolutions of certain polynomials [Elektronische Daten] [Massoud Jahangiri] For α ≥ 0 and β ≥ 0, let K(β) consist of those functions f(z), analytic and non-zero in |z| < 1, such that for θ1 < θ2 < θ1 + 2π and . It is conjectured that for 1 ≤ α ≤ β and α an integer, the weighted convolution of polynomials having their zeros on |z| = 1 and belonging to K(α, β), also belong to K(α, β). This conjecture is known to be true for the case α = 1, which leads to an alternative proof for the generalised Polya-Schoenberg conjecture. The case α = 2 is also known to be true for cubic polynomials. We prove the conjecture for certain quartic polynomials when 2 ≤ α ≤ 4. Copyright © Australian Mathematical Society 1989 Bulletin of the Australian Mathematical Society Cambridge University Press 40/3(1989-12), 397-405 0004-9727 40:3<397 1989 40 BAZ https://doi.org/10.1017/S0004972700017433 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700017433 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jahangiri Massoud Department of Mathematica University of California Davis CA 95616 United States of America NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 40/3(1989-12), 397-405 0004-9727 40:3<397 1989 40 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge