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On the divergence of Fourier series of functions in several variables

✍ Scribed by L. Gogoladze,V. Tsagareishvili


Book ID
126350059
Publisher
Springer
Year
2013
Tongue
English
Weight
208 KB
Volume
39
Category
Article
ISSN
0133-3852

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Fourier Series of Radial Functions in Se
✍ M.A. Pinsky; N.K. Stanton; P.E. Trapa πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 586 KB

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