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Let $G=G(x,t)$ be the heat kernel on the one-dimensional torus $\mathbb{T}^1,$ with $x \in \mathbb{T}^1$ and $t \in (0,T].$ $G$ is given by \begin{equation} G(x,t) = (4 \pi t)^{-1/2} \sum_{k \in \...

Let $G$ be a compact matrix Lie group with Haar measure $\mu$. Then the heat kernel $\rho: G\times (0,\infty) \rightarrow \mathbb{R}$ satisfies (1) $\rho(g_1g_2,t)=\rho(g_2g_1,t)$ for all positive $t$,...

We consider the stationary Stokes problem in $\mathbb{R}^n$ $$\DeclareMathOperator{\Dvg}{\nabla\cdot} \begin{cases} \Delta u + \nabla p = f & \text{ in $\mathbb{R}^n$} \\ \Dvg u =0. \end{cases} $...