Heat Kernel for the Kohn Laplacian on the Heisenberg Group
Ovidiu L. Calin, Der‐Chen Chang, Kenrô Furutani, Chisato Iwasaki · Applied and numerical harmonic analysis · 2010
We shall deal next with the nonsymmetric form of the Heisenberg group. The Heisenberg group considered in this section will be the set ℍ n = ℝ n ×ℝ n ×ℝ 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 ′ ) ∈ ℝ n ×ℝ n ×ℝ and $$x \cdot {y}^{{\prime}} ={ \sum olimits }_{k=1}^{n}{x}_{ k}{y}_{k}^{{\prime}}.$$