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Results tagged with fa.functional-analysis
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user 6651
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
Why isn't the theorem of approximation applicable in Banach spaces?
EDIT: since I'm not an expert on Banach spaces, I feel I shouldn't say anything more, but anyway; an essential ingredient is an exact formula in Hilbert spaces for $\|x + y\|^2$. Just an idea (perhaps …
- 1,990
2
votes
Accepted
The Frechet derivative and Lagrange multipliers on Banach spaces
NOTE: this was a comment, because I thought it wasn't detailed enough for an answer; but Jules (the OP) specifically asked me to post it as an answer.
NOTE to Jules: However, maybe you should wait a …
- 1,990
5
votes
Does this sequence span $L^2$?
Not an answer, but maybe helpful.
These questions can be much harder than they look. There is a simple-looking, explicit set of functions $\{f_\alpha \} \subset L^2(0,1; dx/x)$ (see Operators, Funct …
- 1,990
2
votes
Existence of weak limits
For functions, the answer is NO, i.e. the limit need not be a function.
Let $I_h=(2h)^{-1} \chi_{[-h,h]}$, so that $I_h$ approximates the Dirac delta as $h \to 0^+$. You are considering $I_h * f_\lam …
- 1,990
18
votes
1
answer
3k
views
Let a function f have all moments zero. What conditions force f to be identically zero?
Throughout, let $f$ be a Lebesgue measurable function (or continuous if you wish, but this is probably no easier). (Questions with distributions etc. are possible also but I want to keep things simple …
- 1,990
12
votes
1
answer
706
views
Parametrisations for null temperature functions: nonuniqueness of solutions to the heat equa...
Disclaimer. I expect this is a highly open problem, but maybe I'm wrong and someone has come up with some answers besides those given here. In any case, all information appreciated, thanks!
Definition …
- 1,990
38
votes
2
answers
13k
views
What, exactly, has Louis de Branges proved about the Riemann Hypothesis?
I know this is a dangerous topic which could attract many cranks and nutters, but:
According to Wikipedia [and probably his own website, but I have a hard time seeing exactly what he's claiming] Louis …
- 1,990