R******y
发帖数: 651 | 1 【 以下文字转载自 Mathematics 讨论区 】
发信人: RICIIkey (昵称太短!), 信区: Mathematics
标 题: complex analysis 中的一个定理
发信站: BBS 未名空间站 (Sun Oct 21 21:27:30 2007)
忘了具体说的是啥。大致是说一个complex variable z, 一个analytic function f(z)
如果 |z*f(z)| goes to zero as z goes to infinite, then infinite contour
integral f(z)dz is zero. 谁给回忆一下这个定理的名字是？印象里是叫做Jordan
theorem？ | i*******n
发帖数: 188 | 2 I don't know the name of this theorem, when we learn the course of complex
analysis there was no name for that.
But Jordan' lemma is a different and stronger theorem, saying that if
f(z) -> 0 as z-> \infty, then
\int f(z) e^{i p z} dz =0 for the infinite contour.
See this:
http://en.wikipedia.org/wiki/Jordan%27s_lemma | x********g
发帖数: 595 | 3 Theorem:
If on a circular arc C of radius R and centr z = 0, zf(z)→0 uniformlly as R
→ ∞, then Lim R→ ∞ ∮c f(z) dz = 0 |
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