Suffridge's convolution theorem for polynomials with zeros in the unit disk (Q312718)

Let \[ Q_n(\lambda;z) := \sum\limits_{k=0}^nC_k^{(n)}(\lambda)z^k := \prod\limits_{j=1}^n\left( 1 + e^{i(2j-n-1)\lambda/2}\right), \] where \(\lambda\in[0,2\pi/n]\), \(n\in\mathbb{N}\). For every pair of polynomials \(F(z) = \sum_{k=0}^nC_k^{(n)}(\lambda)a_kz^k\) and \(G(z) = \sum_{k=0}^nC_k^{(n)}(\lambda)b_kz^k\), we define \[ F\ast_{\lambda}G(z) := \sum_{k=0}^nC_k^{(n)}(\lambda)a_kb_kz^k. \] The author studies the transformation of classes of polynomials with zeros in the closed unit disk with respect to the \(\ast_{\lambda}\)-convolution. The results are closely linked to some of the known results of Suffridge, Ruscheweyh and Sheil-Small.