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Results tagged with fa.functional-analysis
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user 9833
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Accepted
Is this simple-looking weighted poincare-sobolev inequality correct
This inequality is not true. (For $2<p<2^*$, that is. This is how I understood the question.) To see why, imagine that the function $f$ has a huge peak in the area where the weight $w$ is very smal …
- 6,891
24
votes
2
answers
2k
views
Is the Invariant Subspace Problem arithmetic?
Invariant Subspace Conjecture: A bounded operator on a separable Hilbert space has a non-trivial closed invariant subspace.
Can this conjecture be reformulated as an arithmetic statement, that is, $ …
- 6,891
13
votes
Accepted
History of publication of von Neumann's characterization of orthogonally invariant matrix norms
Probably there is no way to know it for certain, but it's a safe bet that this was related to Fritz Noether https://en.wikipedia.org/wiki/Fritz_Noether . He was a brother of Emmy Noether and also a …
- 6,891
2
votes
Complex structure on $L^2(\mathbb R)$ generalizing the Hilbert transform
EDIT: This solution does not satisfy the third condition,
which rules out the Hilbert transform itself. So, this is an answer to
different question. I do not delete it in hope it may be useful for so …
- 6,891
4
votes
Analytic approximations of smooth vector fields
I believe the most natural approach to this particular question is via Fourier analysis. In the periodic case we have the series
$$u(x)=\sum_{k\in\mathbb{Z}^3}u_k e^{2\pi i (k,x)},$$
and the condition …
- 6,891