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Given a global field $F$ and a reductive group $G$, where can I find the spectral decomposition of $$ L^2( Z(\mathbb{A}) G(F) \backslash G( \mathbb{A})).$$

I will need the result in this generality, means for a general reductive group and for function and number fields.

I have just seen some instances of such theorems yet and would be happy about a reference. Of course, I expect that the function field and number field case have been treated, but probably in different places.

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up vote 2 down vote accepted

This is the main aim of the book "Spectral decomposition and Eisenstein series" by Moeglin and Waldspurger, which is based on the original work of Langlands but updated to use more modern notation and techniques. This has a very detailed account of the spectral decomposition theorems in chapter VI.

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