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

We obtain solutions of parabolic second-order differential equations for functions in the class defined on a ramified surface . 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 limi...

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Bibliographic Details
Published inIzvestiya. Mathematics Vol. 82; no. 3; pp. 494 - 511
Main Author Dubravina, V. A.
Format Journal Article
LanguageEnglish
Published Providence London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.06.2018
IOP Publishing
Subjects
Cartesian coordinates
Chernoff's theorem
Differential equations
Feynman formula
Mathematical analysis
parabolic differential equation
ramified surface
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Summary:We obtain solutions of parabolic second-order differential equations for functions in the class defined on a ramified surface . 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.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM8376