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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 409, Pages 5–16 (Mi znsl5508)  
This article is cited in 2 scientific papers (total in 2 papers)

Formal power series and their applications to mathematical theory of diffraction

V. M. Babich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (211 kB) Citations (2)
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Abstract: The formal power series (FPS) coefficients of which are smooth functions are considered. FPS form an algebra over the field $(\mathbb C)$ of complex numbers. It is possible to differentiate FPS. FPS are series having asymptotic character (in accordance with the definition by V. S. Buslaev and M. M. Scriganov). As an example of applications of FPS we consider the geometro-optical expansion for the scalar analog of Rayleigh waves.
Key words and phrases: formal power series, ansatz, ray method, surface wave.
Received: 26.11.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 194, Issue 1, Pages 1–7
DOI: https://doi.org/10.1007/s10958-013-1500-9
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: V. M. Babich, “Formal power series and their applications to mathematical theory of diffraction”, Mathematical problems in the theory of wave propagation. Part 42, Zap. Nauchn. Sem. POMI, 409, POMI, St. Petersburg, 2012, 5–16; J. Math. Sci. (N. Y.), 194:1 (2013), 1–7
Citation in format AMSBIB
\Bibitem{Bab12}
\by V.~M.~Babich
\paper Formal power series and their applications to mathematical theory of diffraction
\inbook Mathematical problems in the theory of wave propagation. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 409
\pages 5--16
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5508}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3032225}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 194
\issue 1
\pages 1--7
\crossref{https://doi.org/10.1007/s10958-013-1500-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899023129}
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  • https://www.mathnet.ru/eng/znsl/v409/p5
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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