Skip to main content
Log in

Representation of green’s function for the heat equation on a compact lie group

  • Published:
Mathematical Notes Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Yosida,Functional Analysis, Berlin (1965).

  2. H. Heyer,Probability Measures on Locally Compact Groups, Springer, Heidelberg (1977).

    MATH  Google Scholar 

  3. M. Malliavin and P. Malliavin, “Integration on loop groups. Quasi-invariant measures,”JFA,93, 207–237 (1990).

    Article  MATH  Google Scholar 

  4. M. Malliavin and P. Malliavin, “Integration on loop groups. Asymptotic Peter-Weyl orthogonality,”JFA,108, 13–46 (1992).

    Article  MATH  Google Scholar 

  5. R. Leandre, “Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces,”J. Geom. Phys., No. 11, 517–528 (1993).

    Google Scholar 

  6. H. Airault and P. Malliavin, “Integration on loop groups. Heat equation for the Wiener measure,”JFA,104, 71–109 (1992).

    Article  MATH  Google Scholar 

  7. S. Albeverio and R. Hoegh-Krohn, “The energy representation of a Sobolev Lie Group,”Compositive Math.,36, 37–52 (1978).

    MATH  Google Scholar 

  8. A. Barut and R. Raczka,Theory of Group Representations and Applications, Warszawa (1977).

  9. R. Feynman, “Space-time approach to nonrelativistic quantum mechanics,”Rev. Mod. Phys.,20, 367 (1948).

    Article  Google Scholar 

  10. E. Nelson, “Feynman integrals and the Schrödinger equations,”J. Math. Phys.,5, 332 (1964).

    Article  MATH  Google Scholar 

  11. O. G. Smolyanov, “Smooth measures on loop groups,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],345, No. 4, 455–458 (1995).

    Google Scholar 

  12. F. W. Warner,Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, New York (1983).

    MATH  Google Scholar 

  13. É. B. Vinberg,Compact Lie Groups [in Russian], Izd. Moskov. Univ., Moscow (1967).

    Google Scholar 

  14. A. D. Wentzel,A Course in the Theory of Random Processes [in Russian], Nauka, Moscow (1996).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 397–413, March, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02676670

Key words

Navigation