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Results tagged with real-analysis
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user 12482
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
8
votes
Accepted
Is there dual space of the distributions $\mathcal{D}'(R)$?
Well, that depends on what topology you want to put on the space of distributions. The weak$^*$ is probably not really the one you would like to take. Instead, the strong dual might be more useful. Th …
- 8,098
14
votes
Which functions have all derivatives everywhere positive?
Well, there are certainly more. If you look at the chain rule then you see that the $n$-th derivative is a linear combinations of products of derivatives of the two functions you compose with positive …
- 8,098
6
votes
analysis over non-Archimedean ordered fields
Well, there seems to be a lot of literature. I have encountered similar questions once when discussing problems in deformation quantization. here the ordered field is simply the field of formal Lauren …
- 8,098
11
votes
3
answers
2k
views
Hilbert's 17th Problem for smooth functions
Consider an open subset $U \subseteq \mathbb{R}^n$ and a smooth function $f\colon U \longrightarrow \mathbb{R}$ with $f(x) \ge 0$ for all $x \in U$.
It is then known (if I remember correctly: by Mich …
- 8,098