Timeline for Reference for Kronecker-Weyl theorem in full generality
Current License: CC BY-SA 4.0
17 events
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| Oct 29, 2020 at 5:25 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 27, 2020 at 19:20 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 27, 2020 at 19:19 | history | rollback | Günter Rote |
Rollback to Revision 8
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| Oct 27, 2020 at 19:17 | history | edited | Günter Rote | CC BY-SA 4.0 |
correction
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| Oct 27, 2020 at 17:11 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 25, 2020 at 6:52 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 25, 2020 at 6:38 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 24, 2020 at 9:03 | history | edited | Günter Rote | CC BY-SA 4.0 |
Added the statement of Thm.18 (specialized) from Weyl [1916]
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| Oct 22, 2020 at 8:25 | comment | added | Günter Rote | Bailleul continues his sentence: "... so we provide a proof in an appendix" (p.4). If you look in the appendix, you find the independence assumption right at the beginning (p.29). Also in Theorem 1.2. | |
| Oct 22, 2020 at 2:10 | comment | added | Peter Humphries | Bailleul is referring to the discrete version of the Kronecker-Weyl theorem on $\mathbb{T}^n$ without the assumption of linear independence. Where does this appear in these references? | |
| Oct 21, 2020 at 23:11 | comment | added | Günter Rote | strange that @A.Bailleul writes "It seems a reference to a proof of the discrete version of the Kronecker-Weyl theorem is hard to find in a published form". totally unaware of the classical Kuipers-Niederreiter book, or the more recent monograph by Drmota and Tichy from 1997, or by Hlawka 1984. (Or why not the proof by Weyl himself?) | |
| Oct 21, 2020 at 22:28 | comment | added | Peter Humphries | @A.Bailleul has also recently given written up nice proofs of both versions: arxiv.org/abs/2007.05763 | |
| Oct 21, 2020 at 22:26 | comment | added | Peter Humphries | There are indeed two versions of the Kronecker-Weyl theorem: the discrete version, for $n \in \mathbb{N}$, and the continuous version, for $t \in \mathbb{R}$. My answer above is for the continuous version; the proof is reproduced from Section 4.3 of my honours thesis drive.google.com/open?id=1YoQpDCO4wvyD9EFxfExEVNmtJkjDxBdv. A proof for the discrete version is given in Appendix A of my masters thesis drive.google.com/open?id=1KW0wdc4Ydh_pupHp9sM3zXPBBnG5gJPp. | |
| Oct 21, 2020 at 20:59 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 21, 2020 at 20:50 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 21, 2020 at 20:45 | history | edited | Günter Rote | CC BY-SA 4.0 |
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| Oct 21, 2020 at 18:54 | history | answered | Günter Rote | CC BY-SA 4.0 |