Timeline for Rearrangements of a power series at the boundary of convergence
Current License: CC BY-SA 3.0
14 events
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| Mar 26, 2015 at 5:07 | comment | added | Ryan Budney | This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. | |
| Mar 26, 2015 at 5:03 | comment | added | Srinivas K | I'm a bit confused. For all permutations $\sigma$, $f_{\sigma}$ gives the same function inside the disc of convergence. So, by identity theorem, there is only one analytic function with that power series. Therefore, the set of possible functions contains only one analytic function. Is this correct ? | |
| Mar 26, 2015 at 2:57 | comment | added | Yemon Choi | How does this address the original question? | |
| Jan 3, 2015 at 8:10 | comment | added | Andrés E. Caicedo | @AlexandreEremenko It is difficult. The question is stated precisely. If the word "space" is confusing you, just read "collection" instead. | |
| Dec 8, 2014 at 15:32 | comment | added | Alexandre Eremenko | Before we decide whether it is difficult or not, state your question precisely. I do not understand what is a "space of functions" in which each function is defined on its own set. | |
| Dec 8, 2014 at 10:24 | comment | added | echinodermata | @AlexandreEremenko some rearrangements could converge on different sets than others, and some could have a very very nasty set of convergence; in its full generality, the problem asks you to consider them all, with no restrictions whatsoever on converging everywhere, almost everywhere, etc. But since that seems difficult, feel free to restrict the scope of the problem to try to make progress. | |
| Dec 7, 2014 at 16:38 | comment | added | Alexandre Eremenko | Some rearangements will diverge at some points. When you say "a space of functions" do you consider only those rearrangements that converge everywhere? Or almost everywhere? | |
| Nov 4, 2014 at 6:14 | history | edited | echinodermata |
Added cv tag
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| Feb 14, 2014 at 9:54 | history | migrated | from math.stackexchange.com (revisions) | ||
| Feb 14, 2014 at 9:54 | comment | added | Willie Wong | By OP request + in regards to @AndresCaicedo's comment above, migrating to MO. | |
| Feb 13, 2014 at 14:45 | comment | added | Andrés E. Caicedo | Hi. It has been suggested that you repost your question on MathOverflow, including a link to the version here indicating that no answers have yet been received. It would increase the exposure of the question with the experts that may have something to say about it. As I said, I doubt a full answer is known, but even partial results may be interesting and shed some light on the key difficulties. | |
| Jan 19, 2014 at 6:24 | answer | added | user68061 | timeline score: 1 | |
| Jan 19, 2014 at 6:12 | comment | added | Andrés E. Caicedo | Great question. | |
| Jan 19, 2014 at 4:33 | history | asked | echinodermata | CC BY-SA 3.0 |