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Results tagged with ca.classical-analysis-and-odes
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user 13093
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
0
votes
When is perimeter continuous under Hausdorff convergence?
I found a paper which deals with the case I'm interested. It shows that for the particular case of minimal relative perimeter sets with given volume constraint the relative perimeter of the minimizers …
- 2,222
7
votes
3
answers
706
views
When is perimeter continuous under Hausdorff convergence?
It is known that the perimeter is lower semicontinuous for the convergence of sets. Two variants are widely known:
(Golab's theorem) in $\Bbb{R}^2$ if the sets $\Omega_n$ converge to $\Omega$ in the …
- 2,222
5
votes
2
answers
715
views
Darboux function on $[0,1]$ with interesting property
I have proved a few years ago the following proposition:
There exists $f: [0,1] \to [0,1]$ with Darboux property such that there exist $A,B \subset[0,1]$ with $A\cap B=\emptyset,\ A \cup B=[0,1]$ …
- 2,222
4
votes
2
answers
592
views
Pseudo-alternate series
Suppose $(a_n)$ is a non-increasing sequence of positive real numbers and $\varepsilon_i = \{\pm 1\},\ \forall i \in \mathbb{N}$ such that $\sum\limits_{i=1}^\infty \varepsilon_i a_i$ is convergent.
I …
- 2,222