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Zapiski Nauchnykh Seminarov LOMI, 1976, Volume 62, Pages 27–38 (Mi znsl2033)  
Asymptotic behavior of the Fourier coefficients for the problem of scattering on contours $r=(1+\beta\cos\varphi)^\gamma$

R. G. Barantsev, V. V. Grudtsyn
Full-text PDF (496 kB) (1)
Abstract: In this paper the analytic properties of the wave function in the region bounded by the scattering body are studied. This problem is of major importance for the development of the analytic side of the method of separation of variables in problems with noncoordinate boundaries. New asymptotic estimates for the Fourier coefficients of the scattered field are obtained. They indicate the analyticity of the wave function in the physical plane for all $r>0$.
English version:
Journal of Soviet Mathematics, 1979, Volume 11, Issue 5, Pages 680–686
DOI: https://doi.org/10.1007/BF01455045
Bibliographic databases:
UDC: 534.26
Language: Russian
Citation: R. G. Barantsev, V. V. Grudtsyn, “Asymptotic behavior of the Fourier coefficients for the problem of scattering on contours $r=(1+\beta\cos\varphi)^\gamma$”, Mathematical problems in the theory of wave propagation. Part 8, Zap. Nauchn. Sem. LOMI, 62, "Nauka", Leningrad. Otdel., Leningrad, 1976, 27–38; J. Soviet Math., 11:5 (1979), 680–686
Citation in format AMSBIB
\Bibitem{BarGru76}
\by R.~G.~Barantsev, V.~V.~Grudtsyn
\paper Asymptotic behavior of the Fourier coefficients for the problem of scattering on contours $r=(1+\beta\cos\varphi)^\gamma$
\inbook Mathematical problems in the theory of wave propagation. Part~8
\serial Zap. Nauchn. Sem. LOMI
\yr 1976
\vol 62
\pages 27--38
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=471629}
\zmath{https://zbmath.org/?q=an:0333.35059}
\transl
\jour J. Soviet Math.
\yr 1979
\vol 11
\issue 5
\pages 680--686
\crossref{https://doi.org/10.1007/BF01455045}
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