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Results tagged with ca.classical-analysis-and-odes
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user 75
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
8
votes
Does the "continuous locus" of a function have any nice properties?
It's a standard result that the continuous locus is always $G_\delta$. For each $r>0$, let $U(r)$ be the set of points $x$ such that some neighborhood of $x$ maps into some ball of radius $r$. Then …
- 4,217
28
votes
Accepted
Which sequences can be extended to analytic functions? (e. g., Ackermann's function)
It's a standard theorem in complex analysis that if $z_n$ is a sequence that goes to infinity, there is an entire function taking any prescribed values at the $z_n$. There is a function $f$ vanishing …
CommunityBot
- 1
2
votes
Construction of a convex function nondifferentiable on a countable set
If you think in terms of constructing the derivative of $f$ rather than $f$ itself, you're looking for an increasing function that has an arbitrary countable set $H$ of discontinuities. There's a sta …
- 31.2k
7
votes
Is there a topology on growth rates of functions?
I might be misremembering, but I believe the question of whether there is a cofinal totally ordered sequence of growth rates is independent of ZFC. It follows from CH (or more generally, Martin's Axi …
- 31.2k
4
votes
Accepted
Abelianization of Lie groups
I don't have anything to say about specific examples, but here are some general remarks. A way to construct the abelianization of any compact group is to consider its image under the product of all i …
- 31.2k