TITLE: Two-sided Laplace transform
QUESTION [5 upvotes]: I want to study more formally the properties of the two sided Laplace transform 
$$
\hat f(z)=\int_{-\infty}^{\infty} f(t)e^{zt}dt
$$
as a kind of generalization of the Fourier transform. I found some good references in the books by LePage and van der Pol, but these are operational calculus books, and I would like a more mathematical approach, well defined spaces, etc... 
Where can I find something (books, articles) like that?

REPLY [2 votes]: I found it sometime ago. Advanced Mathematical Analysis by Richard Beals has a really good mathematical formulation of the two-sided Laplace transform, definition spaces and others.