Timeline for Behaviour of power series on their circle of convergence
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2021 at 21:47 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Math Jaxed
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| Dec 15, 2010 at 18:16 | comment | added | Gerald Edgar | $\sum z^n/n^2$ converges on the whole circle. | |
| Dec 15, 2010 at 18:00 | comment | added | Kevin O'Bryant | Any finite set? I've never seen an example that achieves $S=\emptyset$. | |
| Dec 15, 2010 at 10:48 | vote | accept | Piotr | ||
| Dec 14, 2010 at 18:00 | comment | added | Andrés E. Caicedo | @Gerald : Anyway, the real issue is that even for Fourier series, I do not think we have the kind of very detailed pointwise control that the question requires (we would need a stronger version of Carleson's theorem, perhaps; the analysts I've asked did not seem too hopeful in this regard). | |
| Dec 14, 2010 at 17:48 | comment | added | Andrés E. Caicedo | @Gerald: The issue is that many of the trigonometric series that appear here are not Fourier series. | |
| Dec 14, 2010 at 17:26 | comment | added | Gerald Edgar | Note the mention of Fourier series: If power series $\sum a_n z^n$ has radius of convergence 1, write $z=e^{i\theta}$ to get a Fourier series, whose set of divergence (in the real line) you are interested in. | |
| Dec 14, 2010 at 17:25 | answer | added | Andrés E. Caicedo | timeline score: 70 | |
| Dec 14, 2010 at 16:27 | comment | added | Gideon Schechtman | Until Andres return you can look at the paper below (can be found by google search) which has a lot of information. In particular any $G_\delta$ set and any $F_\sigma$ sets of logarithmic measure zero is a set of divergence. Erdös, Paul; Herzog, Fritz; Piranian, George, Sets of divergence of Taylor series and of trigonometric series. Math. Scand. 2, (1954). 262–266. | |
| Dec 14, 2010 at 15:56 | comment | added | S. Carnahan♦ | If your countable set is closed, then a suitable series is relatively easy to construct. | |
| Dec 14, 2010 at 15:11 | history | asked | Piotr | CC BY-SA 2.5 |