Volterra parametrix correction
= Volterra parametrix correction
{c}
{title2=$H=P+P*\sum_{k\ge1}(-1)^kR^{*k}$}
If $R=(\partial_t+\Delta_x)P$ is smooth and bounded up to time zero on a <closed manifold>, the <Volterra convolution of kernels> solves $Q+R+R*Q=0$ by $Q=\sum_{k\ge1}(-1)^kR^{*k}$. Bounds by $C^k\operatorname{vol}(M)^{k-1}t^{k-1}/(k-1)!$ prove convergence. Then $H=P+P*Q$ is the exact <Riemannian heat kernel> and has the same initial delta limit.