Funktsional'nyi Analiz i ego Prilozheniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 2, Pages 25–39 (Mi faa3517)  

This article is cited in 4 scientific papers (total in 4 papers)

Probabilistic Approximation of the Evolution Operator

I. A. Ibragimovab, N. V. Smorodinaab, M. M. Faddeevab*

a St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia

Abstract: A method for approximation of the operator $e^{-itH}$, where $H=-\frac{1}{2}\frac{d^2}{dx^2}+V(x)$, in the strong operator topology is proposed. The approximating operators have the form of expectations of functionals of a certain random point field.

Keywords: evolution equation, limit theorem, Feynman–Kac formula.

Funding Agency Grant Number
Russian Science Foundation 17-11-01136
Russian Foundation for Basic Research 16-01-00258
I. A. Ibragimov acknowledges the financial support of the Russian Foundation for Basic Research (project no. 16-01-00258). N. V. Smorodina (who authors the results of Section 3) acknowledges the support of the Russian Science Foundation (project no. 17-11-01136). M. M. Faddeev (who authors the results of Section 4) acknowledges the support of the Russian Science Foundation (project no. 17-11-01136).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/faa3517

Full text: PDF file (247 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2018, 52:2, 101–112

Bibliographic databases:

UDC: 519.2
MSC: 28C20, 60H05, 60G57
Received: 31.08.2017

Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Probabilistic Approximation of the Evolution Operator”, Funktsional. Anal. i Prilozhen., 52:2 (2018), 25–39; Funct. Anal. Appl., 52:2 (2018), 101–112

Citation in format AMSBIB
\Bibitem{IbrSmoFad18}
\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper Probabilistic Approximation of the Evolution Operator
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 2
\pages 25--39
\mathnet{http://mi.mathnet.ru/faa3517}
\crossref{https://doi.org/10.4213/faa3517}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3799410}
\elib{https://elibrary.ru/item.asp?id=32837035}
\transl
\jour Funct. Anal. Appl.
\yr 2018
\vol 52
\issue 2
\pages 101--112
\crossref{https://doi.org/10.1007/s10688-018-0216-5}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000437825500003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049584842}


Linking options:
  • http://mi.mathnet.ru/eng/faa3517
  • https://doi.org/10.4213/faa3517
  • http://mi.mathnet.ru/eng/faa/v52/i2/p25

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Approximation of the evolution operator by expectations of functionals of sums of independent random variables”, Theory Probab. Appl., 64:1 (2019), 12–26  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. V. Platonova, S. V. Tsykin, “Ob odnoi predelnoi teoreme, svyazannoi s resheniem zadachi Koshi dlya uravneniya Shrëdingera s operatorom drobnogo differentsirovaniya poryadka $\alpha\in\bigcup\limits_{m=3}^{\infty}(m-1, m)$”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 254–264  mathnet
    3. M. V. Platonova, S. V. Tsykin, “Probabilistic approximation of the solution of the Cauchy problem for the higher-order Schrödinger equation”, Theory Probab. Appl., 65:4 (2021), 558–569  mathnet  crossref  crossref  isi
    4. V M. Platonova , V S. Tcykin, “Probabilistic approximation of the evolution operator e-ith where”, Dokl. Math., 101:2 (2020), 144–146  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:342
    Full text:18
    References:32
    First page:28

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021