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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.
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 …
- 31.2k
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 …
- 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
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