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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.

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  • $\begingroup$ The Laplace/Mellin transform is a major topic of the theory of $\zeta(s)$ and more generally of complex analysis, a tangential field is distribution theory (and functional analysis). $\endgroup$ – reuns Sep 3 '19 at 22:22
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You can check:

  1. Debnat Integral transforms and their applications.CRC Press
  2. Davies Integral transforms and their applications. Springer GTM
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