Fourier-Laplace级数的缺项算术平均在Lebesgue点处的收敛性  

Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points

作　　者：戴峰[1] 王昆扬[1] 

机构地区：[1]北京师范大学数学系,北京100875

出　　处：《数学学报（中文版）》2003年第4期729-732,共4页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(19771009)

摘　　要：设f(x)为定义于n-维欧氏空间R^n中的单位球面∑(n-1)上的Lebesgue可积函数,σ_N~δ(f)表示f的Fourier-Laplace级数的Cesaro平均.众所周知,λ:=(n-2)/2是Cesaro平均的临界阶.本文就n是偶数的情形证明了,使得1/N∑_(k=1)~Nσ_(n_k)~λ(f)(x)→f(x),N→∞,在每个满足一定对极条件的Lebesgue点成立的具有一定“缺项程度”的数列{n_k}的存在性。Let n-a be the sphere in an n-dimensional Euclidean space Rn. For a function f ∈ L(n-i) denote by σNδ(f) the Cesaro means of order δof the Fourier-Laplace series of f. The special value λ:=n-2/2 of δ is known as the critical index. In the case of n is even, this paper proves the existence of the 'rare' sequence {nk} such that the summability takes place at each Lebesgue point satisfying some antipole conditions (see [1-8]).

关 键 词：收敛性 FOURIER-LAPLACE级数 球调和 Lebesgue点 

分 类 号：O174.41[理学—数学]