A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group
A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group
Let $\mathcal {L}_\gamma = -\frac {1}{4} \left ( \sum _{j=1}^n(X_j^2+Y_j^2)+i\gamma T \right )$ where $\gamma \in \mathbb {C}$, and $X_j$, $Y_j$ and $T$ are the left-invariant vector fields of the Heisenberg group structure for $\mathbb {R}^n \times \mathbb {R}^n\times \mathbb {R}$. We explicitly compute the Fourier transform (in the spatial …