Wei Zhiyong, Zhu Yongtai. The Extended Jordan’s Lemma and the Relation between Laplace Transform and Fourier Transform[J]. Applied Mathematics and Mechanics, 1997, 18(6): 531-534.
 Citation: Wei Zhiyong, Zhu Yongtai. The Extended Jordan’s Lemma and the Relation between Laplace Transform and Fourier Transform[J]. Applied Mathematics and Mechanics, 1997, 18(6): 531-534.

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

• Rev Recd Date: 1996-05-13
• Publish Date: 1997-06-15
• 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 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.
•  [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

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