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Solution of the Cauchy Problem for the Heat Equation on the Heisenberg Group and the Wiener Integral

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Abstract

The issues related to applications of functional integrals to evolution equations are studied. In particular, this is the problem of representation of solutions to the Cauchy problem for the heat equation in the three-parameter Heisenberg group H3(ℝ) in terms of Wiener integral in the space of trajectories from C[0, t] × C[0, t].

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References

  1. A. Hulanicki, “The Distribution of Energy in the Brownian Motion in the Gaussian Field,” Stud. math. 56 (2), 165 (1976).

    Article  MathSciNet  Google Scholar 

  2. B. Gaveau, “Principe de Moindre Action, Propagation de la Chaleur et Estimées sous Elliptiques sur Certains Groupes Nilpotents,” Acta math. 139 (1–2), 95 (1977).

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  3. S. Vatanabe, “Analysis of Wiener Functionals (Malliavin Calculus) and it’s Applications to Heat Kernels,” Ann. Probab. 15 (1), 1 (1987).

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  4. S. V. Mamon, “Wiener Measure on the Heisenberg Group and Parabolic Equations,” Fund. Prikl. Matem. 21 (4), 67 (2016).

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Acknowledgments

The author is grateful of his scientific advisor E. T. Shavgulidze for formulation of the problem and valuable remarks during preparation of the paper.

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Authors and Affiliations

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

    S. V. Mamon

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  1. S. V. Mamon
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Correspondence to S. V. Mamon.

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Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2019, Vol. 74, No. 6, pp. 8–14.

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Mamon, S.V. Solution of the Cauchy Problem for the Heat Equation on the Heisenberg Group and the Wiener Integral. Moscow Univ. Math. Bull. 74, 221–226 (2019). https://doi.org/10.3103/S0027132219060020

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  • DOI: https://doi.org/10.3103/S0027132219060020

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