Remarks on the preceding paper by Gavin Brown and Edwin Hewitt (Q802098)

The paper mentioned in the title [Math. Ann. 268, 91-122 (1984; Zbl 0537.42002)] establishes some sufficient conditions for positive sequences \(\{a_ n:\) \(n=0,1,2,...\}\) which imply inequalities for trigonometric series of the form \(\sum^{N}_{n=0}a_ n \cos n\theta >0\) for \(0\leq \theta <\pi,\) and \(\sum^{2N+1}_{n=1}a_ n \sin n\theta >0\) for \(0<\theta <\pi.\) The author discusses these inequalities from the point of view of sums of Jacobi polynomials. He points out a related result of \textit{St. Ruscheweyh} [SIAM J. Math. Anal. 2, 682-686 (1978; Zbl 0391.30010)].