Laplace 变换存在的第二充分条件及象函数解析性

摘要

先引入Laplace变换存在的第二充分条件,然后给其存在性的一种证明,并进一步证明在第二充分条件下,象函数F(s)在半平面Re(s)>c(>0)内解析,且F′(s)=L[-tf(t)].而F(s)的导数及F(s)的高阶导数在求F(s)及其逆变换时是很有用的,因此,弄清函数f(t)的Laplace变换存在性、可导性及其运算规律是非常必要的.最后,将第二充分条件加以推广.%In this papaer, the second sufficient condition for the existenceof Laplace transform is derived from paper and a kind of proof is given, and it is proved that image function F(s ) is analytic when Re(s)>c (c>0) under the second sufficient condition . Both the derivative and high order derivatives of F(s) are very useful for finding the function F(s) and its inverse transformation, so, it is indispe nsable to cerify the existence and derivability of the laplace transformation of f(t) and try to find a rule of operation for it. Finally, the second suffic ient condition is extended.