Estimate of the remainder in the asymptotic solution of an extremal problem involving nonnegative trigonometric polynomials (Q509077)

Let \(K(\gamma)=\inf_\alpha\{-\min_x\sum_{k=1}^\infty\alpha_k\cos(kx)\}\), for real sequences \(\alpha=(\alpha_1;\dots)\) with either \(\alpha_k=0\) or \(\alpha_k\geq 1\) and \(\sum_{k=1}^\infty\alpha_k=\gamma\), and \(K^{\downarrow}(\gamma)\) is the \(K(\gamma)\) for decreasing sequences \(\alpha\). The given paper is one in a series of papers by the author, where he obtains estimates for these quantities. The \(K(\gamma)\) was introduced by \textit{A. M. Odlyzko} [J. Lond. Math. Soc., II. Ser. 26, 412--420 (1982; Zbl 0476.30005)].