Geodesic
The focussing problem and spectral function asymptotics of Laplace-- Beltrami operator.~II
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 14-53

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The subject of the paper is the construction of formal high frequency solution of the source problem in the neighbourhood of a reflecting boundary. The boundary is geodesically concave. It gives the possibility to use diffraction methods by V. A. Fock. and J. B. Keller. The formal solution of the source problem is applied to obtain the asymptotics of spectral function of Laplace–Beltrami operator. 
@article{ZNSL_1979_89_a1,
     author = {V. M. Babich},
     title = {The focussing problem and spectral function asymptotics of {Laplace--} {Beltrami} {operator.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {14--53},
     publisher = {mathdoc},
     volume = {89},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a1/}
}
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V. M. Babich. The focussing problem and spectral function asymptotics of Laplace-- Beltrami operator.~II. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 14-53. http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a1/