Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points |
| |
Authors: | Feng Dai Kun Yang Wang |
| |
Institution: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China, E-mail: wangky@bnu.edu.cn, CN |
| |
Abstract: | Let ∑
n
−1 be the unit sphere in the n-dimensional Euclidean space ℝ
n
. For a funcion ƒ∈L(∑
n
−1) denote by σδ
N
(ƒ) the Cesàro means of order δ of the Fourier-Laplace series of ƒ. The special value of δ is known as the critical index. In the case when n is even, this paper proves the existence of the ‘rare’ sequence {n
k
} such that the summability
takes place at each Lebesgue point satisfying some antipole conditions.
Received June 28, 1999, Revised August 11, 1999, Accepted February 16, 2000 |
| |
Keywords: | Convergence Fourier-Laplace series Spherical harmonics Lebesgue point |
本文献已被 SpringerLink 等数据库收录! |
|