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Heat Kernel for the Kohn Laplacian on the Heisenberg Group

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

Abstract

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
$$x \cdot {y}^{{\prime}} ={ \sum \nolimits }_{k=1}^{n}{x}_{ k}{y}_{k}^{{\prime}}.$$

Keywords

Fourier Transform Differential Operator Fundamental Solution Heat Kernel Heisenberg Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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