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On the Heat Kernel of a Left Invariant Elliptic Operator

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Excursions in Harmonic Analysis, Volume 2

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

The goal of this chapter is to find the heat kernel of a left invariant operator on a Lie group, by using a geometric method involving Hamiltonian formalism.

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Notes

  1. 1.

    This operator resembles the Grushin operator \(\frac{1} {2}(x_{2}^{2}\partial _{x_{1}}^{2} + \partial _{x_{2}}^{2})\), but in this case it is left invariant with respect to a group law.

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Acknowledgements

This research project is partially supported by an NSF grant DMS-1203845 and Hong Kong RGC competitive earmarked research grants #600607, #601410.

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Authors and Affiliations

  1. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, 48197, USA

    Ovidiu Calin

  2. Department of Mathematics and Department of Computer Science, Georgetown University, Washington, D.C., 20057, USA

    Der-Chen Chang

  3. Department of Mathematics, Fu Jen Catholic University, Taipei, 242, Taiwan, ROC

    Der-Chen Chang

  4. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

    Yutian Li

Authors
  1. Ovidiu Calin
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  2. Der-Chen Chang
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  3. Yutian Li
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Corresponding authors

Correspondence to Ovidiu Calin or Der-Chen Chang .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, 20742-0001, Maryland, USA

    Travis D. Andrews

  2. Norbert Wiener Center, Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Radu Balan

  3. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    Wojciech Czaja

  5. , Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Kasso A. Okoudjou

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Calin, O., Chang, DC., Li, Y. (2013). On the Heat Kernel of a Left Invariant Elliptic Operator. In: Andrews, T., Balan, R., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8379-5_10

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