An extremal problem and inequalities for entire functions of exponential type
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- by Andrés Chirre, Dimitar K. Dimitrov, Emily Quesada-Herrera and Mateus Sousa;
- Proc. Amer. Math. Soc. 152 (2024), 3299-3318
- DOI: https://doi.org/10.1090/proc/16764
- Published electronically: June 12, 2024
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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 Carathéodory–Fejér–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.References
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Bibliographic Information
- Andrés Chirre
- Affiliation: Departamento de Ciencias - Sección Matemáticas, Pontificia Universidad Católica del Perú, Lima, Perú
- ORCID: 0000-0003-1724-7221
- Email: cchirre@pucp.edu.pe
- Dimitar K. Dimitrov
- Affiliation: Departamento de Matemática, IBILCE, Universidade Estadual Paulista UNESP, São José do Rio Preto 15054, Brazil
- MR Author ID: 308699
- Email: d_k_dimitrov@yahoo.com
- Emily Quesada-Herrera
- Affiliation: Graz University of Technology, Institute of Analysis and Number Theory, Kopernikusgasse 24/II, 8010 Graz, Austria
- MR Author ID: 1509564
- ORCID: 0000-0003-2704-740X
- Email: quesada@math.tugraz.at
- Mateus Sousa
- Affiliation: BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Bizkaia, Spain
- MR Author ID: 1273391
- ORCID: 0000-0002-1748-1803
- Email: mcosta@bcamath.org
- Received by editor(s): April 19, 2023
- Received by editor(s) in revised form: November 7, 2023
- Published electronically: June 12, 2024
- Additional Notes: Research was supported by the Brazilian Science Foundations FAPESP under Grants 2016/09906-0, 2019/12413-4 and 2021/13340-0 and CNPq under Grant 309955/2021-1, the Bulgarian National Research Fund through Contract KP-06-N62/4, and the Austrian Science Fund (FWF) via Project P-35322. The fourth author was supported by the grant Juan de la Cierva incorporación 2019 IJC2019-039753-I, the Basque Government through the BERC 2022-2025 program, by the Spanish State Research Agency project PID2020-113156GB-100/AEI/10,13039/501100011033 and through BCAM Severo Ochoa excellence accreditation SEV-2023-2026.
- Communicated by: Yuan Xu
- © Copyright 2024 by Carlos Andrés Chirre Chávez; Dimitar K. Dimitrov; Emily Quesada-Herrera; Mateus Sousa
- Journal: Proc. Amer. Math. Soc. 152 (2024), 3299-3318
- MSC (2020): Primary 42A38, 30D15, 41A17
- DOI: https://doi.org/10.1090/proc/16764
- MathSciNet review: 4767264