Geodesic
An analog of Rudin's theorem for continuous radial positive definite functions of several variables
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 172-179 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mathscr G_m$ be the class of radial real-valued functions of $m$ variables with support in the unit ball $\mathbb B$ of the space $\mathbb R^m$ that are continuous on the whole space $\mathbb R^m$ and have a nonnegative Fourier transform. For $m\ge3$, it is proved that a function $f$ from the class $\mathscr G_m$ can be presented as the sum $\sum f_k\widetilde\ast f_k$ 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.
Keywords: positive definite functions, multidimensional radial functions, Rudin's theorem. 
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A. V. Efimov. An analog of Rudin's theorem for continuous radial positive definite functions of several variables. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 172-179. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a15/

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