Bessel级数在边界解析点处的性态  

BEHAVIOUR OF BESSEL SERIES AT AN ANALYTIC POINT OF THE BOUNDARY

作　　者：木乐华[1] ALoushoushNizar 

机构地区：[1]山东大学数学系,济南250100

出　　处：《山东大学学报（自然科学版）》1999年第4期393-397,共5页Journal of Shandong University(Natural Science Edition)

摘　　要：给出圆域中贝塞尔级数的部分和偏差的一个新的表达式。Let D be the disc ｜ ζ ｜<1 and Γ the circle ｜ ζ ｜=1. Denote Bessel functions and Neumann polynomials by J n(z),O n(z) respectively. If f(z) is analytic in D and continuous on D ,then we say f∈A(D) .The series A 0(f)2+∑∞1A n(f)J n(z) (A n(f)=12π i ∮Γf(ζ)O n(ζ) d ζ ) is called the Bessel series expansion of f on D ,its partial sums are denoted by S (B) n(f;z), n=0,1,2,…. Theorem Let p be a non-negative integer.If f∈A(D) and f is analytic at a point z 0∈Γ ,then S (B) n(f;z 0)-f(z 0)=o(1n p). If we only know f∈A(D) ,then for z∈Γ, S (B) n(f;z)-f(z)=o( ln nn p). Here we can see the influence of f being analytic at z 0∈Γ .

关 键 词：BESSEL级数 边界解析点 性态 christoffel公式 解析性 贝塞尔级数 部分和 解析函数 

分 类 号：O174.55[理学—数学]