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Heat Kernels for Elliptic and Sub-elliptic Operators pp 225–271Cite as

Heat Kernels for Laplacians and Step-2 Sub-Laplacians

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

Abstract

In this section we shall provide an explicit multiplication form of the Laplacian for a certain class of two-step nilpotent Lie groups including Heisenberg groups; see [46]. The result presented in this section is more precise than the explicit formula of the heat kernel given for the first time in the paper of Hulanicki [68], as explained in Remark 9.1.5.

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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 Statistics, Georgetown University, Washington, DC, 20057, USA

    Der-Chen Chang

  3. Department of Mathematics Science, University of Tokyo, 2641 Yamazaki, Noda, Chiba, 278-8510, Japan

    Kenro Furutani

  4. Department of Mathematical Science, University of Hyogo, 2167 Shosha, Himeji, 671-2201, Japan

    Chisato Iwasaki

Authors
  1. Ovidiu Calin
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  2. Der-Chen Chang
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  3. Kenro Furutani
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  4. Chisato Iwasaki
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Corresponding author

Correspondence to Ovidiu Calin .

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Calin, O., Chang, DC., Furutani, K., Iwasaki, C. (2011). Heat Kernels for Laplacians and Step-2 Sub-Laplacians. In: Heat Kernels for Elliptic and Sub-elliptic Operators. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4995-1_10

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