A note on pointwise convergence for expansions in surface harmonics of higher dimensional Euclidean spaces. (English) Zbl 1173.42003
Summary: We study the Fourier-Laplace series on the unit sphere of higher-dimensional Euclidean spaces and obtain a condition for convergence of Fourier-Laplace series on the unit sphere. The result generalizes Carleson’s theorem to higher-dimensional unit spheres.
MSC:
| 42B05 | Fourier series and coefficients in several variables |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 30G35 | Functions of hypercomplex variables and generalized variables |
