Abstract
An extremal problem for positive definite functions on \({{\mathbb{R}}^{n}}\) with a fixed support and a fixed value at the origin (the class \({{\mathfrak{F}}_{r}}({{\mathbb{R}}^{n}})\)) is considered. It is required to find the least upper bound for a special form functional over \({{\mathfrak{F}}_{r}}({{\mathbb{R}}^{n}})\). This problem is a generalization of the Turán problem for functions with support in a ball. A general solution to this problem for \(n \ne 2\) is obtained. As a consequence, new sharp inequalities are obtained for derivatives of entire functions of exponential spherical type.
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This work was supported by the Russian Science Foundation, grant no. 23-11-00153.
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Translated by I. Ruzanova
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Manov, A.D. On an Extremal Problem for Compactly Supported Positive Definite Functions. Dokl. Math. (2024). https://doi.org/10.1134/S1064562424701965
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DOI: https://doi.org/10.1134/S1064562424701965