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Timeline for Fourier transform on lattice strip

Current License: CC BY-SA 4.0

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Sep 19, 2021 at 16:44 vote accept spaceman
Sep 15, 2021 at 21:09 answer added Mateusz Kwaśnicki timeline score: 2
Sep 15, 2021 at 13:27 history edited YCor
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Sep 15, 2021 at 13:24 comment added spaceman @MateuszKwaśnicki I have edited the question given your comment.
Sep 15, 2021 at 13:23 history edited spaceman CC BY-SA 4.0
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Sep 15, 2021 at 13:06 comment added spaceman @MateuszKwaśnicki Ah yes, I missed that out. I suspect then $L_N$ is a quotient of $L$ and not a subgroup at all. I wish to identify $(N+1+k)a_2$ with $ka_2$. I am essentially repeating the lattice strips vertically. In which case, I suspect that I cannot use the characters of $L$ to obtain the characters of $L_N$.
Sep 14, 2021 at 19:36 comment added Mateusz Kwaśnicki Maybe I misunderstood something: as stated, $L_N$ is not a subgroup of $L$. For example, $a_2, N a_2 \in L_N$, but $a_2 + N a_2 \notin L_N$. One can identify $L_N$ with a factor of $L$ (a homomorphic image of $L$) in a number of ways (essentially by identifying $(N+1) a_2$ with $k a_1$ for an arbitrary $k \in \mathbb Z$), and each of these will correspond to some Pontryagin dual, but I am not sure if this is what you meant.
Sep 13, 2021 at 19:17 history edited spaceman CC BY-SA 4.0
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Sep 13, 2021 at 12:31 history asked spaceman CC BY-SA 4.0