$u \in L^2(R^n)$
I am guessing that $L^2(R^n)$ means the $L^2$ norm over an n-dimensional vector. The context is an energy minimization function : total variation–based model of Rudin, Osher, and Fatemi (ROF)
$u \in L^2(R^n)$
I am guessing that $L^2(R^n)$ means the $L^2$ norm over an n-dimensional vector. The context is an energy minimization function : total variation–based model of Rudin, Osher, and Fatemi (ROF)
$L^2(\mathbb{R}^n)$ is the space of all measurable functions $f\colon \mathbb{R}^n \to \mathbb{R}$ (or possibly $f\colon \mathbb{R}^n \to \mathbb{C}$) such that $ \int_{\mathbb{R}^n} |f|^2 \;<\; \infty\text{,} $ where the integral is a Lebesgue integral. (The square root of this integral is the 2-norm of $f$.)