Timeline for Basic obstruction to anything like holomophic symmetric functions of infinitely many variables?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 8, 2023 at 18:10 | comment | added | David Feldman | In general a path in ordered-zero-set space space that induces a permutation on the zeros, so a loop in unordered-zero-set space will drag along an discrete invariants attached to the zeros. | |
| Oct 8, 2023 at 16:41 | comment | added | David Feldman | If you have a tie between the modulus of two zeros, then a perturbation could flip how they stand in the order, causing a discontinuity in the choice of elementary factors, right? | |
| Oct 7, 2023 at 18:51 | comment | added | Vik78 | I don't see why the Weierstrass factorization theorem can't apply in a canonical way. You can just choose an ordering on the zero set in order of nondecreasing modulus, and choose your elementary factors $E_{p_n}$ with $p_n = n$. See Conway, Functions of One Complex Variable, theorems VII.5.12 and VII.5.15. For whatever natural complex structure you choose on the spaces involved I expect this section would be analytic. | |
| Oct 7, 2023 at 18:23 | history | edited | David Feldman | CC BY-SA 4.0 |
added 3 characters in body
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| Oct 5, 2023 at 17:00 | comment | added | David Feldman | I was trying not to be too specific in case someone knew a relevant theorem. But I'd be happy with the Hausdorff metric. I'd be happy with considering first sequences, considering them in the product (topology) of countably many disks, then taking a quotient by the action of the full symmetric group. | |
| Oct 5, 2023 at 13:43 | comment | added | Christian Remling | What topology on the discrete subsets of $D$ do you have in mind here? | |
| Oct 5, 2023 at 5:58 | history | asked | David Feldman | CC BY-SA 4.0 |