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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 438, Pages 83–94 (Mi znsl6185)  
This article is cited in 1 scientific paper (total in 1 paper)

The equation of convolution on a large finite interval with the symbol which has zeros of nonintegral powers

A. M. Budylin, S. B. Levin

St. Petersburg State University, St. Petersburg, Russia
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Abstract: We study one equation of convolution on a large finite interval. This equation arose in acoustics for a description of a wave conductor surface with a bed of ice. The main feature of this equation is that the symbol of the corresponding operator has zeros of nonintegral degrees on the dual variable so that the inverse operator is a long-range one. We found power-order complete asymptotic expansion for a kernel of the inverse operator as a length of the interval tends to infinity.
Key words and phrases: semiclassical asymptotics, singular integral equations, Wiener-Hopf method, Schwartz alternating method.
Funding agency Grant number
Saint Petersburg State University 11.38.263.2014
Russian Foundation for Basic Research 14-01-0076015 А
Received: 12.10.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 1, Pages 54–62
DOI: https://doi.org/10.1007/s10958-017-3393-5
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. M. Budylin, S. B. Levin, “The equation of convolution on a large finite interval with the symbol which has zeros of nonintegral powers”, Mathematical problems in the theory of wave propagation. Part 45, Zap. Nauchn. Sem. POMI, 438, POMI, St. Petersburg, 2015, 83–94; J. Math. Sci. (N. Y.), 224:1 (2017), 54–62
Citation in format AMSBIB
\Bibitem{BudLev15}
\by A.~M.~Budylin, S.~B.~Levin
\paper The equation of convolution on a~large finite interval with the symbol which has zeros of nonintegral powers
\inbook Mathematical problems in the theory of wave propagation. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 438
\pages 83--94
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6185}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3501068}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 1
\pages 54--62
\crossref{https://doi.org/10.1007/s10958-017-3393-5}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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