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Formal power series and their applications in the mathematical theory of diffraction. (English. Russian original) Zbl 1303.78003

J. Math. Sci., New York 194, No. 1, 1-7 (2013); translation from Zap. Nauchn. Sem. POMI 409, 5-16 (2012).
Summary: Formal power series (FPS) the coefficients of which are smooth functions are considered. The FPS form an algebra on the field of complex numbers \((\mathbb C)\). One can differentiate the FPS. The FPS are series having an asymptotic nature (in accordance with the definition by V. S. Buslaev and M. M. Skriganov [Teor. Mat. Fiz. 19, 217–232 (1974; Zbl 0291.35020); translation in Theor. Math. Phys. 19(1974), 465–476 (1975; Zbl 0296.35023)]). As an example of applications of the FPS, the geometro-optical expansion for the scalar analog of Rayleigh waves is considered.

MSC:

78A45 Diffraction, scattering
35C20 Asymptotic expansions of solutions to PDEs
78M35 Asymptotic analysis in optics and electromagnetic theory
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