Geodesic
Solution of the Cauchy problem for the heat equation on the Heisenberg group and the Wiener integral
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2019), pp. 8-14 
S. V. Mamon. Solution of the Cauchy problem for the heat equation on the Heisenberg group and the Wiener integral. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2019), pp. 8-14. http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a1/
@article{VMUMM_2019_6_a1,
     author = {S. V. Mamon},
     title = {Solution of the {Cauchy} problem for the heat equation on the {Heisenberg} group and the {Wiener} integral},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--14},
     year = {2019},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a1/}
}
TY  - JOUR
AU  - S. V. Mamon
TI  - Solution of the Cauchy problem for the heat equation on the Heisenberg group and the Wiener integral
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 8
EP  - 14
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a1/
LA  - ru
ID  - VMUMM_2019_6_a1
ER  - 
%0 Journal Article
%A S. V. Mamon
%T Solution of the Cauchy problem for the heat equation on the Heisenberg group and the Wiener integral
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 8-14
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a1/
%G ru
%F VMUMM_2019_6_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $H_3(\mathbb{R})$ in terms of Wiener integral in the space of trajectories from $C[0,t]\times C[0,t]$.

[1] Hulanicki A., “The distribution of energy in the Brownian motion in the Gaussian field”, Stud. math., 56:2 (1976), 165–173 | DOI | MR | Zbl

[2] Gaveau B., “Principe de moindre action, propagation de la chaleur et estimees sous elliptiques sur certains groupes nilpotents”, Acta math., 139:1–2 (1977), 95–153 | DOI | MR | Zbl

[3] Vatanabe S., “Analysis of Wiener functionals (Malliavin calculus) and it's applications to heat kernels”, Ann. Probab., 15:1 (1987), 1–39 | DOI | MR

[4] Mamon S.V., “Mera Vinera na gruppe Geizenberga i parabolicheskie uravneniya”, Fund. i prikl. matem., 21:4 (2016), 67–98 | MR