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Results tagged with fa.functional-analysis
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user 49551
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
1
answer
2k
views
Sobolev Space, "characteristic function" for the weak derivative
Let $\Omega$ be an open bounded subset of $\mathbb{R}^N$, working in the space $H_0^1(\Omega)$ with the inner product
$$(u,v)_{H_0^1} = \int_\Omega \nabla u \cdot \nabla v$$
for $u\in H_0^1$ and $\mu …
- 485
3
votes
1
answer
303
views
$f: [0,1]\rightarrow L^1(\Omega)$ as a (measurable?) function from $[0,1]\times \Omega\right...
Given a map from $\big([0,1], \mathcal{B}[0,1], m\big)$ to a Banach space $(X, \|\cdot \|)$. There are strong measurable functions (they are the point wise a.e. limit of simple functions) and weak mea …
- 485