【摘要】 先引入 L aplace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 .更多还原

【Abstract】 In this papaer, the second sufficient condition for the existence of 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 indispensable 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 sufficient condition is extended.更多还原