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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 78–81
DOI: https://doi.org/10.31857/S2686954320020198
(Mi danma54)
 

MATHEMATICS

Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$

M. V. Platonovaab, S. V. Tsykina

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Saint-Petersburg, Russian Federation
b Saint Petersburg State University, Saint-Petersburg, Russian Federation
References:
Abstract: Two approaches are suggested for constructing a probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$, in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach, the approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables with finite moments of order $2m+2$.
Keywords: Schrödinger equation, Poisson random measures, limit theorems.
Presented: I. A. Ibragimov
Received: 17.12.2019
Revised: 17.12.2019
Accepted: 26.02.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 144–146
DOI: https://doi.org/10.1134/S1064562420020192
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: M. V. Platonova, S. V. Tsykin, “Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 78–81; Dokl. Math., 101:2 (2020), 144–146
Citation in format AMSBIB
\Bibitem{PlaTsy20}
\by M.~V.~Platonova, S.~V.~Tsykin
\paper Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 491
\pages 78--81
\mathnet{http://mi.mathnet.ru/danma54}
\crossref{https://doi.org/10.31857/S2686954320020198}
\zmath{https://zbmath.org/?q=an:1474.60176}
\elib{https://elibrary.ru/item.asp?id=42860669}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 2
\pages 144--146
\crossref{https://doi.org/10.1134/S1064562420020192}
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