The orthogonal complements of $H^1(\mathbb{R})$ in its regular Dirichlet extensions

Yuncong Shen, Liping Li, Jiangang Ying

Consider the regular Dirichlet extension $(\mathcal{E},\mathcal{F})$ for one-dimensional Brownian motion, that $H^1(\mathbb{R})$ is a subspace of $\mathcal{F}$ and $\mathcal{E}(f,g…