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 contribution||An analog of Rudin's theorem for continuous radial positive definite functions of several variables|
|Number of pages||7|
|Journal||Труды института математики и механики УрО РАН|
|Publication status||Published - 2012|
- 27.00.00 MATHEMATICS
Level of Research Output
- VAK List