AN EXTREMAL PROBLEM AND INEQUALITIES FOR ENTIRE FUNCTIONS OF EXPONENTIAL TYPE - Chirre, Andrés; Dimitrov, Dimitar K. [UNESP]; Quesada-Herrera, Emily; Sousa, Mateus (American Mathematical Society (AMS), 2024)
We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath eodory-Fej er- Turán 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.
Keywords: entire function of exponential type; extremal function; extremal problem; One-delta problem