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Some trigonometric extremal problems and duality

Part of: Normed linear spaces and Banach spaces; Banach lattices Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

Szilárd GY. Révész
Szilárd GY. Révész
Affiliation:
Mathematical Institute Hungarian Academy of Sciences Budapest, POB 127, 1364, Hungary
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Abstract

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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 used functional analysis.

Keywords

trigonometrical extremal problemsBorel measures of the d-dimensional torusseparation of convex setsRiesz representation theorem

MSC classification

Secondary: 42A05: Trigonometric polynomials, inequalities, extremal problems 46B25: Classical Banach spaces in the general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 3 , June 1991 , pp. 384 - 390
Copyright
Copyright © Australian Mathematical Society 1991

References

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[2]Révész, Sz. Gy., ‘On Beurling's prime number theorem’, preprint, Mathematical Institute of the Hungarian Academy of Sciences, No. 5, 1990.Google Scholar
[3]Révész, Sz. Gy., ‘Extremal problems and a duality phenomenon’, Proceedings of the IMACS conference held in Dalian, China, 1989, edited by Law, Alan G., to appear.Google Scholar
[4]Révész, Sz. Gy., Polynomial extremal problems (in Hungarian), (thesis for the “candidate degree”, 1988, Budapest).Google Scholar
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