Neumann-Bessel级数的线性求和及其收敛性  

Linear sums and its convergence properties of Neumann-Bessel series.

作　　者：葛金辉[1] 赵江[1] 何甲兴[2] 

机构地区：[1]通化师范学院数学系,吉林通化134002 [2]吉林大学数学系,吉林长春130000

出　　处：《浙江大学学报（理学版）》2005年第2期124-126,共3页Journal of Zhejiang University（Science Edition）

摘　　要：研究了Neumann-Bessel级数部分和的收敛性及其逼近性质.为进一步改进其收敛性和逼近性质,首先从Neumann- Bessel级数部分和出发,构造了一类新的积分算子Hn(f ,z) =18πi∮Γ(f (ζeih) +2 f (ζ) +f (ζe- ih) ) kn(z,ζ) dζ,其中h =π/ (n +1) ,并证明了:若f (z)在Γ上连续,则Hn(f ,z) - f (z) =oωf ,1n ,z∈Γ,其中“o”与n无关,ω(f ,δ)为f (z)在Γ上的连续模.进而得出Hn(f ;z)在单位圆周Γ(|z|=1)上一致地收敛到每个连续的f (z)且其逼近性质优于Fejér和σn(f ,z) .The research into the convergence and the approximating property of sums of Neumann-Bessel has been made to get a further improvement of it. Starting from sums of Neumann-Bessel series, it is constructed that a new integral operator, of it \%H\-n(f,z)=18\%πi\%∮\-Γ(f(ζ\%e i\%h )+2f(ζ)+f(ζ\%e -i\%h ))k\-n(z,ζ)\%d\%ζ, z∈Γ\%, of it \%h=\%π\%/(n+1)\%, which is improved: if \%f(z\%) is continuous on \%Γ\%, that, \%H\-n(f,z)-f(z)=oωf,1n, z∈Γ\%, '\%o\%' and \%n\% unrelated, \%ω(f,δ)\% is the continuous module of \%f(z)\% on \%Γ\%, then gets \%H\-n(f;z)\% converge consistently to each \%f(z)\% continuous on \%Γ(|z|=1)\% of circumference unit, and the approximating property is prior to Fejér sums \%σ\-n(f,z)\%.

关 键 词：Neumann—Bessel级数 线性求和 一致收敛 

分 类 号：O174.21[理学—数学]