An extremal problem and inequalities for entire functions of exponential type
type: Item
instance of: scholarly article
title: An extremal problem and inequalities for entire functions of exponential type
zbMATH Open document ID: 1541.41008
author: Andrés Chirre
author: Dimitar K. Dimitrov
author: Emily Quesada-Herrera
author: Mateus Sousa
published in: Proceedings of the American Mathematical Society
publication date: 2024-07-03T00:00:00Z
review text: The task addressed in this article is bounding integrals of functions of exponential type \(f\) by their values at the origin; those values must not be zero and the integrands nonnegative. The integrals are over the whole real axis. This makes them a so-called one-delta-function. The infimum \(\mathcal{A}\) of these upper bounds are also required. In the classical case the solution is \(\mathcal{A}=1\) and the argmin function is the square of the sinc function.\N\NAn advanced problem of this type is when the integrands are explicitly required to be radially monotone, i.e., increasing/decreasing for the arguments going from \(-\infty\) to \(0\) and from the origin to \(+\infty\), respectively. This problem is solved with \(\mathcal{A}\in(1.2750,1.27714)\).
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 7875283
zbMATH Keywords: one-delta problem
zbMATH Keywords: extremal problem
zbMATH Keywords: extremal function
zbMATH Keywords: entire function of exponential type
MaRDI profile type: Publication
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DOI: 10.1090/PROC/16764
description: scientific article; zbMATH DE number 7875283