On Pointwise Convergence of Fourier Series of the Indicator Function of D Dimensional Ball

作者：Kuratsubo Shigehiko^*

来源：Journal of Fourier Analysis and Applications, 2010, 16(1): 52-59.

DOI：10.1007/s00041-009-9071-3

• Fourier series
• Spherical partial sum
• Indicator function
• Lattice points problem
• Pinsky phenomenon

We prove the pointwise convergence of the Fourier series for the indicator function in d dimensional ball. The results are very different for every dimension. Our method of proof depends on the lattice points problem, especially, on the papers of Czechoslovakian mathematician BA (TM) etislav Novak.

• 出版日期2010-2