Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1983), pp. 49-53
Citer cet article
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/
@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},
year = {1983},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a10/}
}
TY - JOUR
AU - V. P. Smolich
TI - The spectrum of the perturbed Laplace operator on the fundamental domain of a discrete group on the Lobachevskii plane
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1983
SP - 49
EP - 53
IS - 2
UR - http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a10/
LA - ru
ID - VMUMM_1983_2_a10
ER -
%0 Journal Article
%A V. P. Smolich
%T The spectrum of the perturbed Laplace operator on the fundamental domain of a discrete group on the Lobachevskii plane
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1983
%P 49-53
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a10/
%G ru
%F VMUMM_1983_2_a10
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.
