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Feynman Formulas for Solutions to Evolution Equations in Domains of Multidimensional Ramified Surfaces

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Abstract

Solutions of second-order parabolic differential equations for functions defined in domains of a K ramified surface in the class L2(K) are obtained. With the help of Chernoff’s theorem, such solutions (if they exist) can be represented in the form of Lagrangian Feynman formulas, i.e., in the form of limits of integrals over Cartesian powers of the configuration space as the number of factors tends to infinity.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    V. A. Dubravina

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  1. V. A. Dubravina
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Correspondence to V. A. Dubravina.

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Original Russian Text © V.A. Dubravina, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 5.

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Dubravina, V.A. Feynman Formulas for Solutions to Evolution Equations in Domains of Multidimensional Ramified Surfaces. Dokl. Math. 98, 612–615 (2018). https://doi.org/10.1134/S1064562418070220

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  • DOI: https://doi.org/10.1134/S1064562418070220

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