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Results tagged with real-analysis
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user 171439
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
2
votes
1
answer
446
views
A periodic integral inequality
(This problem comes in connection with a geometric problem exposed here.)
Let $\gamma(x,y)$ be a (real) function on the unit disk such that
$$
\frac{\partial^2\gamma}{\partial x \, \partial y} = 0\:\: …
- 134
2
votes
Asymptotic of an improper integral
Note that $\displaystyle\int_0^h \left(\log \frac{1}{u}\right)^{\!1/2} \, \mathrm{d}p(u)\rightarrow 0$ as $h\rightarrow 0$, and that $p(h) \left(\log \dfrac{1}{h}\right)^{1/2}\rightarrow 0$ as $h\rig …
- 134
3
votes
1
answer
340
views
Shrinking a disk with fixed differential
Consider mappings $f$ from $\mathbb{R}^2$ to $\mathbb{R}^2$ with differential
\begin{align}
\mathsf{d} f= \begin{pmatrix}
\cos\psi(x) &\cos\phi(y) \\
\sin \psi(x)& \sin\phi(y)
\end{pmatrix},
\e …
- 134