Geodesic
Explicit representation of the~Green's function for the~three-dimensional exterior Helmholtz equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 163-174

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We construct a sequence of solutions of the exterior Helmholtz equation such that their restrictions form an orthonormal basis on a given surface. The dependence of the coefficients of these functions on the coefficients of the surface are given by an explicit algebraic formula. In the same way, we construct an explicit normal derivative of the Dirichlet Green's function. We also construct the Dirichlet-to-Neumann operator. We prove that the normalized coefficients are uniformly bounded from zero.
Mots-clés : explicit solution
Keywords: Helmholtz exterior problem, Green's function, Dirichlet-to-Neumann operator. 
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     author = {J. P. Cruz and E. L. Lakshtanov},
     title = {Explicit representation of {the~Green's} function for the~three-dimensional exterior {Helmholtz} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--174},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a0/}
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J. P. Cruz; E. L. Lakshtanov. Explicit representation of the~Green's function for the~three-dimensional exterior Helmholtz equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 163-174. http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a0/