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Izvestiya: Mathematics, 2018, Volume 82, Issue 3, Pages 494–511
DOI: https://doi.org/10.1070/IM8376 (Mi im8376) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Representation of solutions of evolution equations on a ramified surface by Feynman formulae

V. A. Dubravina

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (299 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM8376
Abstract: We obtain solutions of parabolic second-order differential equations for functions in the class $L_1(K)$ defined on a ramified surface $K$. By using Chernoff's theorem, we prove that such solutions, whenever they exist, can be represented by Lagrangian Feynman formulae, that is, they can be written as limits of integrals over Cartesian powers of the configuration space as the number of factors tends to infinity.
Keywords: Feynman formula, parabolic differential equation, ramified surface, Chernoff's theorem.
Received: 02.04.2015
Revised: 21.07.2017
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2018, Volume 82, Issue 3, Pages 49–68
DOI: https://doi.org/10.4213/im8376
Bibliographic databases:
Document Type: Article
UDC: 517.1
MSC: 81S40, 81Q30, 46T12
Language: English
Original paper language: Russian
Citation: V. A. Dubravina, “Representation of solutions of evolution equations on a ramified surface by Feynman formulae”, Izv. RAN. Ser. Mat., 82:3 (2018), 49–68; Izv. Math., 82:3 (2018), 494–511
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM8376
  • https://www.mathnet.ru/eng/im/v82/i3/p49
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:429
    Russian version PDF:44
    English version PDF:4
    References:40
    First page:29
     
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