Timeline for Linear combinations of geometric series
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2022 at 14:16 | answer | added | James Propp | timeline score: 1 | |
| Mar 31, 2022 at 2:07 | comment | added | Joseph Van Name | You may post the official answer to your own question. | |
| Mar 28, 2022 at 17:51 | comment | added | James Propp | @Joseph Van Name : I like your answer (though it makes me wish I'd thought harder before posting my question; I've worked with this very same vector space before and forgot I'd done so). Do you want to post it as an official answer, or do you want me to do it? | |
| Mar 28, 2022 at 17:48 | comment | added | James Propp | @Wojowu : Hadn't thought of that; thanks for pointing it out. I don't want answers that rely on the Axiom of Choice. | |
| Mar 27, 2022 at 19:48 | comment | added | Joseph Van Name | I think that the $V'$ will be the sequence of all sequences whose generating functions are just rational functions, and $\sigma$ will just evaluate these rational functions at the point $1$. Alternatively, $V'$ will be the collection of all sums $\mathbf{x}+\mathbf{y}$ where $\mathbf{x}$ satisfies some linear recurrence relation, and $\mathbf{y}$ is zero for all but finitely many terms. Rational generating functions are talked about in Richard Stanley's Enumerative Combinatorics text. | |
| Mar 27, 2022 at 19:09 | comment | added | Wojowu | Any conditions you want to put on this extension? Linear maps can always be extended from one vector space to another, so you can just take $V'=\mathbb C^{\mathbb N}$. | |
| Mar 27, 2022 at 19:07 | history | edited | YCor |
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| Mar 27, 2022 at 19:04 | history | asked | James Propp | CC BY-SA 4.0 |