推广约当引理以及Laplace变换与Fourier变换的对应关系

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The Extended Jordan’s Lemma and the Relation between Laplace Transform and Fourier Transform

Institute of Modern Physics, Academia Sinica, P. O. Box 31, Nanchang Road 253, Lanzhou 730000, P. R. China

摘要: 单变量复变函数积分中用到的约当引理是在||f(Re^iφ||＝0(0≤π)的条件下使用的,而实际上约当引理可以在比较宽松的条件下就可使用,被积函数f(z)除在z的上半平面(Imz≥0)有有限个孤立奇点外,处处解析,且对p>0只要,则这里z=Rei,CR为上半平面的开弧半圆围道,利用推广约当引理可以证明Laplace变换实际上是对应的其复变量函数的Fourier变换。
- 推广约当引理 /
- Laplace变换 /
- Fourier变换 /
- 复变函数
Abstract: Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>0, if =0 where z=Re^iφ and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.
- extended Jordan’s lemma /
- Laplace transform /
- Fourier transform /
- complex variable function

[1]	A.Sveshnikov and A.Tikchonov,The Theory of Functions of a Cmplex Variable,Mir Publisher,Moscow (1978).
[2]	魏志勇、诸永泰.广义约当引理,甘肃科学学报,6(2) (1994),26