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Mathematics of the USSR-Sbornik, 1978, Volume 34, Issue 6, Pages 737–764
DOI: https://doi.org/10.1070/SM1978v034n06ABEH001355 (Mi sm2565) 		 
This article is cited in 17 scientific papers (total in 17 papers)

On the quantization of rapidly oscillating symbols

M. V. Karasev, V. E. Nazaikinskii
English version PDF (1623 kB) Citations (17) Russian version article
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DOI: https://doi.org/10.1070/SM1978v034n06ABEH001355
Abstract: The authors construct a calculus of functions of coordinate and differentiation operators, ordered in an arbitrary manner. The transition from one order to another is studied, and it is shown that linear combinations of functions of this form with exponential oscillating symbols yield global asymptotic solutions of pseudodifferential equations with smooth bicharacteristics. Formulas are obtained for the composition of two operators with oscillating symbols.
Bibliography: 22 titles.
Received: 06.06.1975 and 24.06.1977
Bibliographic databases:
UDC: 517.43
MSC: 47G05, 47A60, 35S10, 81E05
Language: English
Original paper language: Russian
Citation: M. V. Karasev, V. E. Nazaikinskii, “On the quantization of rapidly oscillating symbols”, Math. USSR-Sb., 34:6 (1978), 737–764
Citation in format AMSBIB
\Bibitem{KarNaz78}
\by M.~V.~Karasev, V.~E.~Nazaikinskii
\paper On the quantization of rapidly oscillating symbols
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 6
\pages 737--764
\mathnet{http://mi.mathnet.ru/eng/sm2565}
\crossref{https://doi.org/10.1070/SM1978v034n06ABEH001355}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=503592}
\zmath{https://zbmath.org/?q=an:0391.47036|0417.47025}
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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