Timeline for Reference for discrete Laplacian on $\mathbb{Z}$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2020 at 15:52 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title (the question was bumped anyway); edited tags; edited tags
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| Feb 4, 2020 at 15:45 | history | edited | I love pineapple coffee | CC BY-SA 4.0 |
added 305 characters in body
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| Feb 2, 2020 at 23:52 | comment | added | YCor | Could you be more precise about the space on which you want information about this operator. In particular, are you really interested about your questions in the whole topological vector space $\mathbf{R}^\mathbf{\mathbf{Z}}$? | |
| Feb 2, 2020 at 19:16 | comment | added | Nemo | If you are looking for earliest references then see Phillips and Wiener, "Nets and Dirichlet problem" (1923). | |
| Feb 2, 2020 at 19:07 | comment | added | Christian Remling | Here I'm of course assuming that you defined the operator on $\ell^2(\mathbb Z)$. | |
| Feb 2, 2020 at 19:06 | comment | added | Christian Remling | There won't be any references that discuss this operator at length since it's very easy to analyze: just take Fourier transforms $Fx = \sum x_n e^{int}$ to represent $\Delta$ as multiplication by $2(1-\cos t)$ in $L^2(-\pi,\pi)$. This immediately answers all your questions (for example, the spectrum equals $[0,4]$, is purely ac of multiplicitly $2$). | |
| Feb 2, 2020 at 18:56 | history | asked | I love pineapple coffee | CC BY-SA 4.0 |