Heat Kernel for the Kohn Laplacian on the Heisenberg Group

  • Ovidiu Calin
  • Der-Chen Chang
  • Kenro Furutani
  • Chisato Iwasaki
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We shall deal next with the nonsymmetric form of the Heisenberg group. The Heisenberg group considered in this section will be the set n = n × n × with the following group law:
$$(x,y,t) {_\ast} ({x}^{{\prime}},{y}^{{\prime}},{t}^{{\prime}}) = (x + {x}^{{\prime}},y + {y}^{{\prime}},t + {t}^{{\prime}} + x \cdot {y}^{{\prime}}),$$
where (x, y, t), (x , y , t ) ∈ n × n × and
$$x \cdot {y}^{{\prime}} ={ \sum \nolimits }_{k=1}^{n}{x}_{ k}{y}_{k}^{{\prime}}.$$


Fourier Transform Differential Operator Fundamental Solution Heat Kernel Heisenberg Group 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ovidiu Calin
    • 1
  • Der-Chen Chang
    • 2
  • Kenro Furutani
    • 3
  • Chisato Iwasaki
    • 4
  1. 1.Department of MathematicsEastern Michigan UniversityYpsilantiUSA
  2. 2.Department of Mathematics and StatisticsGeorgetown UniversityWashingtonUSA
  3. 3.Department of Mathematics ScienceUniversity of TokyoNodaJapan
  4. 4.Department of Mathematical ScienceUniversity of HyogoHimejiJapan

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