Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 128-133
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Ya. V. Kurylev. A shortwave source near a smooth, convex hypersurface and the spectral function of the Laplace operator on a Riemannian manifold. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 128-133. http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a8/
@article{ZNSL_1978_78_a8,
author = {Ya. V. Kurylev},
title = {A shortwave source near a smooth, convex hypersurface and the spectral function of the {Laplace} operator on a {Riemannian} manifold},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {128--133},
year = {1978},
volume = {78},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a8/}
}
TY - JOUR
AU - Ya. V. Kurylev
TI - A shortwave source near a smooth, convex hypersurface and the spectral function of the Laplace operator on a Riemannian manifold
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1978
SP - 128
EP - 133
VL - 78
UR - http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a8/
LA - ru
ID - ZNSL_1978_78_a8
ER -
%0 Journal Article
%A Ya. V. Kurylev
%T A shortwave source near a smooth, convex hypersurface and the spectral function of the Laplace operator on a Riemannian manifold
%J Zapiski Nauchnykh Seminarov POMI
%D 1978
%P 128-133
%V 78
%U http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a8/
%G ru
%F ZNSL_1978_78_a8
The Tauberian theorem of B. M. Levitan reduces the question of the asymptotics of the spectral function of the Laplace operator on a smooth Riemannian manifold with boundary to the problem of constructing the asymptotics of a Green function possessing certain additional properties. The paper is devoted to the construction of the appropriate Green function for the case of a geodesically concave boundary.
