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arXiv · 2304.05337

An extremal problem and inequalities for entire functions of exponential type

Andrés Chirre·Dimitar K. Dimitrov·Emily Quesada-Herrera·Mateus Sousa
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Abstract

We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath\'eodory--Fej\'er--Tur\'an problem. The first variation imposes the additional requirement that the function is radially decreasing while the second one is a generalization which involves derivatives of the entire function. Various interesting inequalities, inspired by results due to Duffin and Schaeffer, Landau, and Hardy and Littlewood, are also established.

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Andrés Chirre, Dimitar K. Dimitrov, Emily Quesada-Herrera, Mateus Sousa. 2023-04-11. An extremal problem and inequalities for entire functions of exponential type. https://arxiv.org/abs/2304.05337

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