Answer by Disintegrating By Parts for Linear span in the intersection of...
Let $H_1 = L^2[0,\pi]$, and let let $H_2$ be the subspace of absolutely continuous functions on $[0,2\pi]$ with first derivative in $L^2$ and with Sobolev norm$$ \|f\|_2 =...
View ArticleLinear span in the intersection of Hilbert spaces
Let $V$ be a vector space. Assume $H_1$ and $H_2$ are subspaces of $V$, and that both $H_1$ and $H_2$ are Hilbert spaces with inner-products $\langle \cdot, \cdot\rangle_1$ and $\langle...
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