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Daniele Tampieri
Daniele Tampieri
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I asked myself the following question while preparing a course on power series for 2nd year students. Let F$F$ be the set of power series with convergence radius equal to 1$1$. What subsets S$S$ of the unit circle C$C$ can be realised as S:={x in C, f diverges in x} for f in F $$ S:=\{x \in C: f\text{ diverges in }x\} $$ for $f \in F$? Any finite subset (and possibly any countable subset) of C$C$ can be realised that way. Who knows more on this?

I asked myself the following question while preparing a course on power series for 2nd year students. Let F be the set of power series with convergence radius equal to 1. What subsets S of the unit circle C can be realised as S:={x in C, f diverges in x} for f in F? Any finite subset (and possibly any countable subset) of C can be realised that way. Who knows more on this?

I asked myself the following question while preparing a course on power series for 2nd year students. Let $F$ be the set of power series with convergence radius equal to $1$. What subsets $S$ of the unit circle $C$ can be realised as $$ S:=\{x \in C: f\text{ diverges in }x\} $$ for $f \in F$? Any finite subset (and possibly any countable subset) of $C$ can be realised that way. Who knows more on this?

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Piotr
Piotr
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Behaviour of power series on their circle of convergence

I asked myself the following question while preparing a course on power series for 2nd year students. Let F be the set of power series with convergence radius equal to 1. What subsets S of the unit circle C can be realised as S:={x in C, f diverges in x} for f in F? Any finite subset (and possibly any countable subset) of C can be realised that way. Who knows more on this?