| 强拟凸域上边界摄动的B-M型积分的稳定性; Stability of Bochner-Martinelli Integrals with Perturbation on the Boundary on Strictly Pseudoconvex Domain | |
| 李娜 ; 陈吕萍 | |
| 2009 | |
| 关键词 | B-M型积分 边界摄动 强拟凸域 稳定性 Bochner-Martinelli Integrals boundary perturbation strictly pseudoconvex domain stability |
| 英文摘要 | 为了考察强拟凸域上的b-M型积分,当积分边界发生摄动时,是否仍然稳定,在b-M型积分Φ(φ)(z)=ζ∫∈dφ(ζ)k(ζ,z),z∈d的积分边界引入一个摄动因子r,得到边界摄动的b-M型积分Φr(φ)(z)=ζ∫*∈drφ(ζ*)k(ζ*,z)=T∫∈dφ(T+r(T))k(T+r(T),z).讨论了摄动函数r对全纯函数的b-M公式的影响,得到全纯函数的b-M公式的积分边界受到摄动以后,b-M公式是相对稳定的,并具有形式上的美.同时也得到相关的结论,全纯函数经r摄动以后仍为全纯函数;但强多次调和函数经r摄动以后,未必保持原有性质.并用CAuCHy主值讨论b-M型积分的稳定性,得到边界摄动的b-M型积分是稳定的,可控制的.; In order to study whether the B-M Integrals on strictly pesudoconvex domain were still of stability or not,when perturbated,a perturbation factor r was introduced into the integral boundary of B-M Integral Φ(φ)(z)=∫ζ∈Dφ(ζ)K(ζ,z),z∈D.Then a boundary perturbated B-M Integral was produced.Φr(φ)(z)=∫ζ*∈Drφ(ζ*)K(ζ*,z)=∫t∈Dφ(t+r(t))K(t+r(t),z).After being perturbated on the integral boundary of B-M Formula,B-M Formula is relatively steady and has a formal beauty.At the same time,a perturbated holomorphic function is still holomorphic;but a perturbated strictly plurisubharmonic function may not remain strictly plurisubharmonic.Cauchy Principal Value was introduced to argue the stability of B-M Integrals.As a result,a boundary perturbated B-M Integral is steady and controllable.; 福建省自然科学基金(S0850029;2008J0206);厦门大学科技创新基金(XDKJCX20063019)资助 |
| 语种 | zh_CN |
| 内容类型 | 期刊论文 |
| 源URL | [http://dspace.xmu.edu.cn/handle/2288/119717]  |
| 专题 | 数学科学－已发表论文 |
| 推荐引用方式 GB/T 7714 | 李娜,陈吕萍. 强拟凸域上边界摄动的B-M型积分的稳定性, Stability of Bochner-Martinelli Integrals with Perturbation on the Boundary on Strictly Pseudoconvex Domain[J],2009. |
| APA | 李娜,&陈吕萍.(2009).强拟凸域上边界摄动的B-M型积分的稳定性.. |
| MLA | 李娜,et al."强拟凸域上边界摄动的B-M型积分的稳定性".(2009). |
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