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6 votes
0 answers
220 views

Is the Taylor map continuous?

(Skip to the bolded theorem below for my question, if you'd like) Some context on asymptotic expansions and the Taylor map In the setting of irregular singularities of meromorphic connections on the ...
6 votes
2 answers
347 views

Does there exist a framework for determining if a power series is "differentially algebraic"

It is a well studied problem to take a function $f$ expressed (usually expressed as a solution to a differential equation w/ some initial conditions) and ask if it has an "elementary closed form&...
0 votes
0 answers
77 views

Completeness of a normed space

We consider the set $\mathcal{PC}([-r,0],X)$ $$\mathcal{PC}([-r,0],X):=\{\varphi:[-r, 0] \rightarrow X: \varphi \text{ is continuous everywhere except for a finite number of points } t_* \text{ ...
10 votes
0 answers
845 views

Witt's proof of Gelfand-Mazur / Ostrowski's Theorem

Previously asked on Math Stackexchange without answers. Background: As sort of a hobby, Ernst Witt gave extremely short proofs for famous theorems. This question is about his six-line proof of the ...