Geodesic
Nonspectral singularities of Green's function for the Helmholtz equation in the exterior of an arbitrary convex polygon
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 21-26

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For the case of the exterior of an arbitrary convex polygon, an asymptotic expression is obtained at the physical level of rigor for the nonspectral singularities closest to the axis $\operatorname{Im}k=0$ of Green's function for the Helmholtz equation $(\Delta+k^2)q=0$ (with Neumann boundary conditions). The validity of this asymptotic expression is verified in the limiting case of a segment by analyzing the exact solution obtained by separation of variables. A geometrical interpretation of the asymptotic equations for the eigenfunctions of the Laplace operator in terms of geometrical optics is proposed. 
@article{ZNSL_1976_62_a1,
     author = {V. M. Babich and N. S. Grigor'ev},
     title = {Nonspectral singularities of {Green's} function for the {Helmholtz} equation in the exterior of an arbitrary convex polygon},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {21--26},
     publisher = {mathdoc},
     volume = {62},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a1/}
}
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V. M. Babich; N. S. Grigor'ev. Nonspectral singularities of Green's function for the Helmholtz equation in the exterior of an arbitrary convex polygon. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 21-26. http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a1/