АНАЛОГ ТЕОРЕМЫ РУДИНА ДЛЯ НЕПРЕРЫВНЫХ РАДИАЛЬНЫХ ПОЛОЖИТЕЛЬНО ОПРЕДЕЛЕННЫХ ФУНКЦИЙ НЕСКОЛЬКИХ ПЕРЕМЕННЫХ

Translated title of the contribution: An analog of Rudin's theorem for continuous radial positive definite functions of several variables

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Abstract

Let G be the class of radial real-valued functions of m variables with support in the unit ball of the space that are continuous on the whole space and have a nonnegative Fourier transform. For , it is proved that a function f from the class G can be presented as the sum of self-convolutions of at most countably many real-valued functions f k with support in the ball of radius 1/2. This result generalizes the theorem proved by Rudin under the assumptions that the function f is infinitely differentiable and the functions f k are complex-valued.
Translated title of the contributionAn analog of Rudin's theorem for continuous radial positive definite functions of several variables
Original languageRussian
Pages (from-to)172-179
Number of pages7
JournalТруды института математики и механики УрО РАН
Volume18
Issue number4
Publication statusPublished - 2012

GRNTI

  • 27.00.00 MATHEMATICS

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  • VAK List

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