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
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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.
@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},
publisher = {mathdoc},
volume = {78},
year = {1978},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a8/ %G ru %F ZNSL_1978_78_a8
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/