Coherent and dissipative phenomena induced by transient adsorption of xenon-131 on a glass surface are studied by nuclear magnetic resonance spectroscopy. We report the results of multiple-quantum filtered experiments over a range of temperatures, covering different relaxation regimes. An analysis in terms of an effective Liouvillian is proposed, the complex eigenvalues of which may be directly extracted from the experimental spectra. For this purpose, we apply recently developed techniques for spectral analysis, in particular decimated signal diagonalization. The results are compared with a conventional fit of the multiple-quantum build-up behavior.