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Results tagged with fa.functional-analysis
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user 100163
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
0
votes
Properties of the topology of sequential convergence $\tau_\text{seq}$
I am aware of two general topology textbooks which discuss sequential spaces: (probably there is also discussion in earlier works by e.g. Frechet, Kuratowski...)
General Topology I by Arkhangel'skii …
- 660
0
votes
1
answer
330
views
Reference request: sequential weak* topology on the space of signed Radon measures
Consider the space $\mathcal{M}_{loc} (\mathbb{R}^d)$ of locally finite signed Radon measures, equipped with the weak* topology in duality with $C_b (\mathbb{R}^d)$. It is known that this is space is …
- 406
1
vote
1
answer
186
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Concentration-compactness for Radon measures on a metric space
It is known (see Ch. 4 in Struwe's Variational Methods) that Radon measures on $\mathbb{R}^n$ satisfy the concentration-compactness principle. Does the same hold true for Radon measures on a general m …
- 34.7k
3
votes
0
answers
68
views
Bounding the norm of Sobolev extension operator
If $\Omega$ is a sufficiently nice bounded open set in $\mathbb{R}^d$, it's known that there exists a continuous linear operator $$\mathcal{E}:W^{1,p}(\Omega)\rightarrow W^{1,p}(\mathbb{R}^d)$$ such t …
- 660