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Results tagged with fa.functional-analysis
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user 317800
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
Completeness of the sequence $\left \{ \frac{1}{x+1},\frac{1}{x+2},\frac{1}{x+3}, \dots \rig...
This is just a comment on the present responses which I am adding in the hope that it will be of interest—it will be too long for that format. Firstly, it treats completeness for more general functi …
- 406
6
votes
Accepted
Reference request: sequential weak* topology on the space of signed Radon measures
This is not an answer since I cannot give the references you are requesting for reasons that will soon be apparent but am not entitled to comment. Firstly, there is something fundamentally wrong with …
- 406
2
votes
Accepted
Identification of smooth operators with rapidly decreasing matrices
This is, of course, a long story incorporating many strands but I will try to give a quick overview. Firstly, it is, as so often, convenient to skip to a more general framework. In your case, this …
- 406
3
votes
limit of Riemann-Stieltjes sums as an integral on $\mathscr{H}$
Three comments, but too long:
The statement is correct in the case of a bounded, self-adjoint operator. Riemann sums are defined in the usual way, except that they are being used for functions with …
- 406
1
vote
Given a compact set $K \subset \mathbb{R}^n$, is the space of distributions supported on $K$...
The short answer to your question is yes. There is such a space, that of the locally smooth functions on $K$.
Let us recall that Schwartz defined the space of distributions with support in $K$ not di …
- 406
2
votes
Pontryagin-reflexivity of spaces of continuous functions
This is a bit tangential to your query but I hope that it might be useful. The duality for Banach spaces that you mention is, in my opinion, best expressed in terms of the symmetric one between betwe …
- 406