Please use this identifier to cite or link to this item: http://elar.urfu.ru/handle/10995/50982
Title: A version of Turán's problem for positive definite functions of several variables
Authors: Efimov, A. V.
Issue Date: 2012
Citation: Efimov A. V. A version of Turán's problem for positive definite functions of several variables / A. V. Efimov // Proceedings of the Steklov Institute of Mathematics. — 2012. — Vol. 277. — № SUPPL. 1. — P. 93-112.
Abstract: Let G m(B) be the class of functions of m variables with support in the unit ball B centered at the origin of the space ℝ m, continuous in ℝ m, normed by the condition f(0) = 1, and having a nonnegative Fourier transform. In this paper, we study the problem of finding the maximum value Φ m(a) of normed integrals of functions from the class G m(B) over the sphere S a of radius a, 0 < a < 1, centered at the origin. It is proved that, in this problem, we may restrict our attention to spherically symmetric functions from G m(B). The existence of an extremal function is proved and a representation of this function as the self-convolution of a radial function is obtained. An integral equation is written for a solution of the problem for any m ≥ 3. The values Φ 3(a) are calculated for 1/3 ≤ a < 1. © 2012 Pleiades Publishing, Ltd.
Keywords: MULTIDIMENSIONAL FUNCTIONS
POSITIVE DEFINITE FUNCTIONS
TURÁN'S PROBLEM
URI: http://elar.urfu.ru/handle/10995/50982
Access: info:eu-repo/semantics/restrictedAccess
RSCI ID: 20475620
SCOPUS ID: 84863585374
WOS ID: 000305909000010
PURE ID: 1079100
ISSN: 0081-5438
DOI: 10.1134/S0081543812050100
Appears in Collections:Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

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