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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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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Abstract 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.
AbstractList 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.
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.
Author Dubravina, V. A.
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Cites_doi 10.1134/S1064562411070209
10.1007/b97696
10.1134/S1061920814020113
10.1016/j.physleta.2006.10.029
10.1063/1.1500422
10.1134/S1064562413050153
10.1134/S1061920813030126
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DocumentTitleAlternate Representation of solutions of evolution equations on a ramified surface by Feynman formulae
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O. G. Smolyanov (14) 2011; 441
B. Simon (4) 1974
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B. Simon (5) 1976
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O. G. Smolyanov (1) 2015
A. V. Bulinskii (3) 2003
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Snippet 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...
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...
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StartPage 494
SubjectTerms Cartesian coordinates
Chernoff's theorem
Differential equations
Feynman formula
Mathematical analysis
parabolic differential equation
ramified surface
Title Representation of solutions of evolution equations on a ramified surface by Feynman formulae
URI https://iopscience.iop.org/article/10.1070/IM8376
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Volume 82
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