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Results tagged with hilbert-spaces
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user 40707
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
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For which $f \in L^2([0,1])$ is $f^\perp \cap C^\infty$ dense in $f^\perp$?
Given $f \in L^2([0,1])$, $f \neq 0$, we can consider the orthogonal complement $f^\perp$ . The smooth functions $C^\infty([0,1])$ are dense in $L^2([0,1])$. Is the intersection $f^\perp \cap C^\infty …
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