Geodesic
Problem of focusing and the asymptotics of the spectral function of the Laplace--Beltrami operator.~I
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 3-19

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The connection between the asymptotics of the spectral function and the formal shortwave expansion of the solution of the problem of the asymptotics of the Green function near a geodesically concave boundary of a two-dimensional surface is considered in the paper. 
@article{ZNSL_1978_78_a0,
     author = {V. M. Babich and B. M. Levitan},
     title = {Problem of focusing and the asymptotics of the spectral function of the {Laplace--Beltrami} {operator.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {78},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a0/}
}
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V. M. Babich; B. M. Levitan. Problem of focusing and the asymptotics of the spectral function of the Laplace--Beltrami operator.~I. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 3-19. http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a0/