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Express Dirichlet energy $E_\mu(f) := \int \|\nabla f(x)\|^2 d\mu(x)$ in terms of Fourier in...

Let $\mathbb R^d$ and let $\mu = p(dx)$ be a probability distribution thereupon, with density $p$ (which maybe assumed bounded, etc.). For a continuously differentiable function $f:\mathbb R^d \to \ma …
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What is the standard terminology for the quantity $\|\nabla f\|_{L^2(\mu)} := \sqrt{\int_{\m...

Let $f:\mathbb R^d \to \mathbb R$ be a continuously differentiable function and let $\mu$ be a probability measure on $\mathbb R^d$. Question. What is the standard teminology for the quantity $\|\nab …
dohmatob's user avatar
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