$W^{1,2}(S^1,\mathbb{R}^{2n})$ has trivial orthogonal complement in $L^2(S^1,\mathbb{R}^{2n})$

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$W^{1,2}(S^1,\mathbb{R}^{2n})$ has trivial orthogonal complement in $L^2(S^1,\mathbb{R}^{2n})$ · Prove2Me