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Analogue of Maslov’s Canonical Operator for Localized Functions and Its Applications to the Description of Rapidly Decaying Asymptotic Solutions of Hyperbolic Equations and Systems

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Abstract

An analogue of Maslov’s canonical operator for rapidly decaying functions is defined. The construction generalizes the ∂/∂τ-canonical operator on homogeneous manifolds from distributions to smooth localized functions. The main novelty is that the wave profile must be specified explicitly.

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References

  1. V. P. Maslov, Perturbation Theory and Asymptotic Methods (Mosk. Gos. Univ., Moscow, 1965) [in Russian].

    Google Scholar 

  2. V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics (Nauka, Moscow, 1976; Reidel, Dordrecht, 1981).

    Book  Google Scholar 

  3. S. Yu. Dobrokhotov, P. N. Zhevandrov, V. P. Maslov, and A. I. Shafarevich, Math. Notes 49 (4), 355–365 (1991).

    Article  MathSciNet  Google Scholar 

  4. S. Yu. Dobrokhotov, B. Tirozzi, and A. I. Shafarevich, Math. Notes 82 (5), 713–717 (2007).

    Article  MathSciNet  Google Scholar 

  5. A. I. Allilueva, S. Yu. Dobrokhotov, S. A. Sergeev, and A. I. Shafarevich, Dokl. Math. 92 (2), 548–553 (2015).

    Article  MathSciNet  Google Scholar 

  6. V. E. Nazaikinskii, B. Yu. Sternin, and V. E. Shatalov, Contact Geometry and Linear Differential Equations (Walter de Gruyter, Berlin, 1992).

    Book  MATH  Google Scholar 

  7. V. P. Maslov and M. V. Fedoriuk, Math. Notes 45 (5), 382–391 (1989).

    Article  MathSciNet  Google Scholar 

  8. V. I. Arnol’d, Funct. Anal. Appl. 1 (1), 1–13 (1967).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia

    V. E. Nazaikinskii & A. I. Shafarevich

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    V. E. Nazaikinskii & A. I. Shafarevich

  3. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. I. Shafarevich

  4. National Research Center “Kurchatov Institute”, Moscow, 123182, Russia

    A. I. Shafarevich

Authors
  1. V. E. Nazaikinskii
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  2. A. I. Shafarevich
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Corresponding author

Correspondence to V. E. Nazaikinskii.

Additional information

Original Russian Text © V.E. Nazaikinskii, A.I. Shafarevich, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 6, pp. 611–615.

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Nazaikinskii, V.E., Shafarevich, A.I. Analogue of Maslov’s Canonical Operator for Localized Functions and Its Applications to the Description of Rapidly Decaying Asymptotic Solutions of Hyperbolic Equations and Systems. Dokl. Math. 97, 177–180 (2018). https://doi.org/10.1134/S1064562418020217

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  • DOI: https://doi.org/10.1134/S1064562418020217

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