Révész, Szilárd Gy. Some trigonometric extremal problems and duality. (English) Zbl 0776.42002 J. Aust. Math. Soc., Ser. A 50, No. 3, 384-390 (1991). Summary: In this paper we present a minimax theorem of infinite dimension. The result contains several earlier duality results for various trigonometrical extremal problems including a problem of Fejér. Also the present duality theorem plays a crucial role in the determination of the exact number of zeros of certain Beurling zeta functions, and hence leads to a considerable generalization of the classical Beurling’s Prime Number Theorem. The proof uses functional analysis. Cited in 1 ReviewCited in 2 Documents MSC: 42A05 Trigonometric polynomials, inequalities, extremal problems 49J35 Existence of solutions for minimax problems 46B25 Classical Banach spaces in the general theory 11M41 Other Dirichlet series and zeta functions Keywords:separation of convex sets; Riesz representation theorem; Borel measures; minimax theorem; trigonometrical extremal problems; duality theorem; Beurling zeta functions; Beurling’s Prime Number Theorem PDFBibTeX XMLCite \textit{S. Gy. Révész}, J. Aust. Math. Soc., Ser. A 50, No. 3, 384--390 (1991; Zbl 0776.42002)