Skip to main content
SpringerLink
Log in

Maslov’s canonical operator in abstract spaces

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

Recently, a number of new methods for constructing asymptotic solutions to various evolution equations has been developed. These asymptotic solutions are expressed at each instant of time via an elementy of some smooth manifoldy and an elementf of some Hilbert space\(\mathcal{F}_y \). We study general properties of the mapping that assigns an asymptotic formula to the pair (y, f).

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. P. Maslov,The Complex WKB Method for Nonlinear Equations [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. V. P. Maslov and O. Yu. Shvedov, “The chaos conservation problem in quantum physics,”Russian J. Math. Phys.,4, No. 2, 173–216 (1996).

    MATH  Google Scholar 

  3. V. P. Maslov and O. Yu. Shvedov, “Asymptotics of solutions to the Schrödinger equation for spin systems,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],361, No. 4, 453–457 (1998).

    MATH  Google Scholar 

  4. V. P. Maslov and O. Yu. Shvedov, “The complex WKB method in Fock space,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],340, No. 1, 42–47 (1995).

    Google Scholar 

  5. V. P. Maslov and O. Yu. Shvedov, “On the divergence problem in quantum field theory,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],357, No. 5, 604–608 (1997).

    MATH  Google Scholar 

  6. V. P. Maslov and O. Yu. Shvedov, “Some identities for the asymptotics of solutions to abstract equations,Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],352, No. 2, 167–171 (1997).

    MATH  Google Scholar 

  7. M. V. Karasev and V. P. Maslov,Nonlinear Poisson Brackets. Geometry and Quantization [in Russian], Nauka, Moscow (1991).

    MATH  Google Scholar 

  8. D. P. Zhelobenko and A. I. Shtern,Representations of Lie Groups [in Russian], Nauka, Moscow (1983).

    MATH  Google Scholar 

  9. F. A. Berezin,The Method of Second Quantisation [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  10. F. A. Berezin, “Models of Gross-Neveu type are quantization of a classical mechanics with nonlinear phase space,”Comm. Math. Phys.,63, 131–153 (1978).

    Article  MATH  Google Scholar 

  11. L. G. Yaffe, “LargeN limits as classical mechanics,”Rev. Modern Phys.,54, No. 2, 407–436 (1982).

    Article  Google Scholar 

  12. F. A. Berezin, “General concept of quantization,”Comm. Math. Phys.,40, No. 2, 153–174 (1975).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, USSR

    O. Yu. Shvedov

Authors
  1. O. Yu. Shvedov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 437–456, March, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shvedov, O.Y. Maslov’s canonical operator in abstract spaces. Math Notes 65, 365–380 (1999). https://doi.org/10.1007/BF02675080

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02675080

Key words

Search

Navigation