Abstract
We obtain an explicit formula which presents the solution of the heat equation on a compact Lie group as the limit of finite-to-one convolutions of Green’s function for the heat equation in Euclidean space.
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References
K. Yosida,Functional Analysis, Berlin (1965).
H. Heyer,Probability Measures on Locally Compact Groups, Springer, Heidelberg (1977).
M. Malliavin and P. Malliavin, “Integration on loop groups. Quasi-invariant measures,”JFA,93, 207–237 (1990).
M. Malliavin and P. Malliavin, “Integration on loop groups. Asymptotic Peter-Weyl orthogonality,”JFA,108, 13–46 (1992).
R. Leandre, “Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces,”J. Geom. Phys., No. 11, 517–528 (1993).
H. Airault and P. Malliavin, “Integration on loop groups. Heat equation for the Wiener measure,”JFA,104, 71–109 (1992).
S. Albeverio and R. Hoegh-Krohn, “The energy representation of a Sobolev Lie Group,”Compositive Math.,36, 37–52 (1978).
A. Barut and R. Raczka,Theory of Group Representations and Applications, Warszawa (1977).
R. Feynman, “Space-time approach to nonrelativistic quantum mechanics,”Rev. Mod. Phys.,20, 367 (1948).
E. Nelson, “Feynman integrals and the Schrödinger equations,”J. Math. Phys.,5, 332 (1964).
O. G. Smolyanov, “Smooth measures on loop groups,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],345, No. 4, 455–458 (1995).
F. W. Warner,Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, New York (1983).
É. B. Vinberg,Compact Lie Groups [in Russian], Izd. Moskov. Univ., Moscow (1967).
A. D. Wentzel,A Course in the Theory of Random Processes [in Russian], Nauka, Moscow (1996).
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Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 397–413, March, 2000.
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Smirnova, M.G. Representation of green’s function for the heat equation on a compact lie group. Math Notes 67, 333–347 (2000). https://doi.org/10.1007/BF02676670
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DOI: https://doi.org/10.1007/BF02676670