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Results tagged with hilbert-spaces
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user 123038
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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Complete set of orthonormal functions on $W^{2,2}([0,1]^2, \mathbb{R}^2)$
Consider $L^2([0,1],\mathbb{R})$.
Then,
$$1, \sqrt{2} \cos(2 \pi j x), \sqrt{2} \sin(2 \pi j x ), \quad j =1,2,\ldots$$
is a Schauder basis on $L^2([0,1], \mathbb{R})$.
I am curious, how does this gen …
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