Skip to main content
SpringerLink
Log in

Feynman and quasi-Feynman formulas for evolution equations

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

New methods for obtaining representations of solutions of the Cauchy problem for linear evolution equations, i.e., equations of the form u t '(t, x) = Lu(t, x), where the operator L is linear and depends only on the spatial variable x and does not depend on time t, are proposed. A solution of the Cauchy problem, that is, the exponential of the operator tL, is found on the basis of constructions proposed by the author combined with Chernoff’s theorem on strongly continuous operator semigroups.

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. K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equation (Springer, New York, 2000).

    MATH  Google Scholar 

  2. I. D. Remizov, J. Funct. Anal. 270 (12), 4540–4557 (2016).

    Article  MathSciNet  Google Scholar 

  3. P. R. Chernoff, J. Funct. Anal. 2 (2), 238–242 (1968).

    Article  Google Scholar 

  4. O. G. Smolyanov, London Math. Soc. Lect. Note Ser. 353, 283–302 (2009).

    Google Scholar 

  5. I. D. Remizov. Russ. J. Math. Phys. 19 (3), 360–372 (2012).

    Article  MathSciNet  Google Scholar 

  6. O. G. Smolyanov and E. T. Shavgulidze, Path Integrals (URSS, Moscow, 2015) [in Russian].

    MATH  Google Scholar 

  7. A. S. Plyashechnik, Russ. J. Math. Phys. 19 (3), 340–359 (2012).

    Article  MathSciNet  Google Scholar 

  8. N. N. Shamarov, Tr. Mosk. Mat. O-va 66, 263–276 (2005).

    MathSciNet  Google Scholar 

  9. N. N. Shamarov, J. Math. Sci. (N.Y.) 151 (1), 2767–2780 (2008).

    Article  MathSciNet  Google Scholar 

  10. L. A. Borisov, Yu. N. Orlov, and V. Zh. Sakbaev, in Preprints of the Keldysh Institute of Applied Mathematics (IPM im. M.V. Keldysha, Moscow, 2015), Vol. 57, p. 057.

    Google Scholar 

  11. Yu. N. Orlov, V. Zh. Sakbaev, and O. G. Smolyanov, Proc. Steklov Inst. Math. 285, 222–232 (2014).

    Article  MathSciNet  Google Scholar 

  12. Yu. N. Orlov, V. Zh. Sakbaev, and O. G. Smolyanov, Izv.: Math. 80 (6), 1131–1158 (2016).

    Article  MathSciNet  Google Scholar 

  13. M. S. Buzinov and Ya. A. Butko, Nauka Obrazovaine 8, 135–154 (2012).

    Google Scholar 

  14. I. D. Remizov, Math. Notes 100 (3), 499–503 (2016).

    Article  MathSciNet  Google Scholar 

  15. V. Zh. Sakbaev, Theor. Math. Phys. 191 (3), 886–909 (2017).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    I. D. Remizov

  2. Nizhny Novgorod State University, Nizhny Novgorod, 630600, Russia

    I. D. Remizov

Authors
  1. I. D. Remizov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. D. Remizov.

Additional information

Original Russian Text © I.D. Remizov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 476, No. 1, pp. 17–21.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Remizov, I.D. Feynman and quasi-Feynman formulas for evolution equations. Dokl. Math. 96, 433–437 (2017). https://doi.org/10.1134/S1064562417050052

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562417050052

Search

Navigation