Geodesic
The spectrum of the perturbed Laplace operator on the fundamental domain of a discrete group on the Lobachevskii plane
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1983), pp. 49-53

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Let $C(z)$ be a real valued function decreasing in some sense in the neighbourhoods of the cusps of the fundamental domains and $$ Lu=-y^2\Delta u+C(z)u. $$ Then $\sigma_{\mathrm{ac}}(L)=[1/4,+\infty)$; $\sigma_{\mathrm{sing}}(L)=\varnothing$; $\sigma_{\mathrm{pp}}(L)$ – is a discrete set of eigenvalues of finite multiplicities. 
@article{VMUMM_1983_2_a10,
     author = {V. P. Smolich},
     title = {The spectrum of the perturbed {Laplace} operator on the fundamental domain of a discrete group on the {Lobachevskii} plane},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {49--53},
     publisher = {mathdoc},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a10/}
}
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V. P. Smolich. The spectrum of the perturbed Laplace operator on the fundamental domain of a discrete group on the Lobachevskii plane. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1983), pp. 49-53. http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a10/