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?