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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 2(6), Pages 183–213 (Mi msb2565)  

This article is cited in 13 scientific papers (total in 13 papers)

On the quantization of rapidly oscillating symbols

M. V. Karasev, V. E. Nazaikinskii


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.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:6, 737–764

Bibliographic databases:

UDC: 517.43
MSC: 47G05, 47A60, 35S10, 81E05
Received: 06.06.1975 and 24.06.1977

Citation: M. V. Karasev, V. E. Nazaikinskii, “On the quantization of rapidly oscillating symbols”, Mat. Sb. (N.S.), 106(148):2(6) (1978), 183–213; 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 Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 2(6)
\pages 183--213
\mathnet{http://mi.mathnet.ru/msb2565}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=503592}
\zmath{https://zbmath.org/?q=an:0391.47036|0417.47025}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 6
\pages 737--764
\crossref{https://doi.org/10.1070/SM1978v034n06ABEH001355}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Maslov, V. E. Nazaikinskii, “Asymptotics for equations with singularities in the characteristics”, Math. USSR-Izv., 19:2 (1982), 315–347  mathnet  crossref  mathscinet  zmath
    2. Karasev M., Maslov V., “Global Asymptotic Operators of the Regular Representation”, 257, no. 1, 1981, 33–38  mathscinet  zmath  isi
    3. M. V. Karasev, V. P. Maslov, “Quantization of symplectic manifolds with conical points”, Theoret. and Math. Phys., 53:3 (1982), 1186–1195  mathnet  crossref  mathscinet  zmath  isi
    4. Ahmed lntissar, “A remark on the convergence of Feynman path integrals for Weyl pseudo-differential operators on Rn”, Communications in Partial Differential Equations, 7:12 (1982), 1403  crossref
    5. M. V. Karasev, V. P. Maslov, “Pseudodifferential operators and a canonical operator in general symplectic manifolds”, Math. USSR-Izv., 23:2 (1984), 277–305  mathnet  crossref  mathscinet  zmath
    6. M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Hideki Omori, Yoshiaki Maeda, Akira Yoshioka, “Weyl manifolds and deformation quantization”, Advances in Mathematics, 85:2 (1991), 224  crossref
    8. Sergio Albeverio, Alexei Daletskii, “Asymptotic quantization for solution manifolds of some infinite dimensional Hamiltonian systems”, Journal of Geometry and Physics, 19:1 (1996), 31  crossref
    9. Sergio Albeverio, Alexei Daletskh, “Algebras of Pseudodifferential Operators inL2 Given by Smooth Measures on Hilbert Spaces”, Math Nachr, 192:1 (1998), 5  crossref  mathscinet  zmath  isi
    10. T A Osborn, M F Kondratieva, “Heisenberg evolution WKB and symplectic area phases”, J Phys A Math Gen, 35:25 (2002), 5279  crossref  mathscinet  zmath  adsnasa  elib
    11. M. V. Karasev, T. A. Osborn, “Symplectic areas, quantization, and dynamics in electromagnetic fields”, J Math Phys (N Y ), 43:2 (2002), 756  crossref  mathscinet  zmath  adsnasa  elib
    12. M V Karasev, T A Osborn, “Quantum magnetic algebra and magnetic curvature”, J Phys A Math Gen, 37:6 (2004), 2345  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. M V Karasev, T A Osborn, “Cotangent bundle quantization: entangling of metric and magnetic field”, J Phys A Math Gen, 38:40 (2005), 8549  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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