On a class of extremal problems |
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Authors: | Sz. Gy. Révész |
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Affiliation: | (1) Mathematical Institute, Hungarian Academy of Sciences, P.O.Box 127 Budapest, H-1364, Hungary |
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Abstract: | In the paper we introduce a class of trigonometrical polynomial extremal problems depending on a continuous parameter 0≤r≤1. It turns out that the two border cases r=0 and r=1 are known problems investigated earlier by Kamae, Mendes-France, Ruzsa and the present author. We also introduce another set of extremal problems for measures with similar parametrization, and prove a duality relationship between the two type of extremal quantities. The proof relies on a minimax theorem proved earlier by the author. The known duality results are proved as corollaries. 1980 MS Classification. Primary 42A05; Secondary 46B25, 46N05. |
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