Looking for a rigorous treatment about Laplace transform. I am looking for a book that deal with integral transforms in a very rigorous way, Fourier analysis I discover that functional analysis and Lebesgue Integral books cover the Fourier analysis( With a little piece of abstract algebra ) in a nicely way but I didn´t found nothing similar to this even in complex analysis books about Laplace transfom. I´ll be greatful if somebody know somo good references. 

You can check:


*

*Debnat Integral transforms and their applications.CRC Press 

*Davies Integral transforms and their applications. Springer GTM

