Geodesic
Functional Laplace operator on a $\mathfrak p$"=adic space and Feynman--Kac and Feynman formulas
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 251-259

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Homogeneous closed PDO are constructed which are analogous to the powers of (absolute value of) infinite dimensional Laplacian and acting in Banach spaces of complex-valued functions defined on function spaces over a field of $\mathfrak p$-adic numbers. For elements of semigroups, for which these PDOs are generators, Feynman formulas and Feynman–Kac ones are obtained.
Keywords: Feynman–Kac formulas, Feynman formulas, functional Laplacian, $p$-adic analysis. 
@article{VSGTU_2011_2_a30,
     author = {N. N. Shamarov},
     title = {Functional {Laplace} operator on a  $\mathfrak p$"=adic space and {Feynman--Kac} and {Feynman} formulas},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {251--259},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a30/}
}
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N. N. Shamarov. Functional Laplace operator on a  $\mathfrak p$"=adic space and Feynman--Kac and Feynman formulas. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 251-259. http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a30/