АНАЛОГ ТЕОРЕМЫ РУДИНА ДЛЯ НЕПРЕРЫВНЫХ РАДИАЛЬНЫХ ПОЛОЖИТЕЛЬНО ОПРЕДЕЛЕННЫХ ФУНКЦИЙ НЕСКОЛЬКИХ ПЕРЕМЕННЫХ

科研成果: Article同行评审

摘要

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.
投稿的翻译标题An analog of Rudin's theorem for continuous radial positive definite functions of several variables
源语言Russian
页(从-至)172-179
页数7
期刊Труды института математики и механики УрО РАН
18
4
Published - 2012

GRNTI

  • 27.00.00 MATHEMATICS

Level of Research Output

  • VAK List

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