Answer by Chee for When I can safely assume that a function is a Laplace...
I would suggest the classic book "The Laplace transform" by David Vernon Widder. On its page 310, Theorem 14a states the following: A necessary and sufficient condition that $f(x)$ can be expressed in...
View ArticleAnswer by Zen Harper for When I can safely assume that a function is a...
This kind of question is very interesting, and I too would like to know answers.Sorry to self-publicise; I hope it's not regarded as impolite, but since I have also considered this exact kind of...
View ArticleAnswer by Andrey Rekalo for When I can safely assume that a function is a...
The answer depends on the class of functions $\phi(t):(0,\infty)\to\mathbb R$ where you want to define the Laplace transform. A standard assumption is that$$e^{-ct}\phi(t)\in...
View ArticleAnswer by Stopple for When I can safely assume that a function is a Laplace...
In Audrey Terras'"Harmonic Analysis on Symmetric Spaces and Applications, I" she has on p. 21 the following: Suppose $\exp(-cx)f(x)$ lies in $L^1(\mathbb R)$ and $f(x)$ vanishes for negative $x$....
View ArticleWhen I can safely assume that a function is a Laplace transform of other...
If I have a function and I want to represent it as being the Laplace transform of another, that is, I want to be sure that there is $\hat{f}(s)$ such that my function $f(x)$ can be written as:$$f(x) =...
View ArticleAnswer by Daniele Tampieri for When I can safely assume that a function is a...
The question has already an accepted answer, but nevertheless I think that the recent result of Buriánková, Edmunds and Pick [1] can give more insight. Precisely, they prove the following resultTheorem...
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