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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
23
votes
4
answers
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Most general definition of differentiation
There are various differentiations/derivatives.
For example,
Exterior derivative $df$ of a smooth function $f:M\to \mathbb{R}$
Differentiation $Tf:TM\to TN$ of a smooth function between manifolds $ …
1
vote
1
answer
601
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What is the difference between $L^2(\mathbb{R})$ and $L^2(\mathbb{R}^2)$? [closed]
$L^2(\mathbb{R})$ and $L^2(\mathbb{R}^2)$ are isometrically isomorphic because both are infinite-dimensional separable Hilbert spaces.
If a Hilbert space $H$ is $L^2(\mathbb{R})$ or $L^2(\mathbb{R}^2 …