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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.
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
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
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
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