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Compactness of the congruence group of measurable functions in several variables

✍ Scribed by A. M. Vershik; U. Haböck


Publisher
Springer US
Year
2007
Tongue
English
Weight
172 KB
Volume
141
Category
Article
ISSN
1573-8795

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We prove that the spherical partial sums of the Fourier series of the indicator function of a ball inside the cube of width \(2 \pi\) converge at the center of the ball if and only if the dimension is strictly less than three. For more general radial functions in three dimensions we give a necessary