On the spectral Theorem of Langlands

We show that the Hilbert subspace of $L^2(G(F)\mathrm{\backslash }G(\text{A}))$ generated by wave packets of Eisenstein series built from discrete series is the whole space. Together with the work of Lapid \cite{L1}, it achieves a proof of the spectral theorem of Langlands based on the work of Bernstein and Lapid \cite{BL} on the meromorphic continuation of Eisenstein series. I have to say that I was unable to complete the proof of an earlier version. Instead, I use truncation on compact sets, as Arthur did to prove the Local Trace Formula in \cite{Alt}.