Skip to main content
SpringerLink
Log in

Maslov's Canonical Operator in Problems on Localized Asymptotic Solutions of Hyperbolic Equations and Systems

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

An analog of Maslov's canonical operator is defined for functions localized in a neighborhood of subsets of positive codimension.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. E. Nazaikinskii and A. I. Shafarevich, “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. Ross. Akad. Nauk 479 (6), 611–615 (2018) [Dokl. Math. 97 (2), 177–180 (2018)].

    MathSciNet  MATH  Google Scholar 

  2. V. E. Nazaikinskii, V. G. Oshmyan, B. Yu. Sternin, and V. E. Shatalov, “Fourier integral operators and the canonical operator,” Uspekhi Mat. Nauk 36 (2(218)), 81–140 (1981) [Russian Math. Surveys 36 (2), 93–161 (1981)].

    MathSciNet  MATH  Google Scholar 

  3. V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation for Equations of Quantum Mechanics (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

  4. V. I. Arnol'd, “Characteristic class entering in quantization conditions,” Funktsional. Anal. Prilozhen. 1 (1), 1–14 (1967) [Functional Anal. Appl. 1(1), 1–13(1967)].

    Article  Google Scholar 

  5. L. Hormander, The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators (Springer-Verlag, Berlin, 1985).

    MATH  Google Scholar 

  6. M. V. Fedoryuk, Saddle-Point Method (Nauka, Moscow, 1977) [in Russian].

    MATH  Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research under grant 17-01-00644 and by the program “Leading Scientific Schools” under grant NSh-6399.2018.1.

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526, Russia

    V. E. Nazaikinskii & A. I. Shafarevich

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, 141701, Russia

    V. E. Nazaikinskii & A. I. Shafarevich

  3. Lomonosov 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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Shafarevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. E. Nazaikinskii or A. I. Shafarevich.

Additional information

Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 3, pp. 424–435.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nazaikinskii, V.E., Shafarevich, A.I. Maslov's Canonical Operator in Problems on Localized Asymptotic Solutions of Hyperbolic Equations and Systems. Math Notes 106, 402–411 (2019). https://doi.org/10.1134/S0001434619090098

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434619090098

Keywords

Search

Navigation