Timeline for Finite-dimensional approximations of the shift operator
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2016 at 14:08 | comment | added | Yemon Choi | Could you explain why you have accepted an answer which does not provide a "good" approximation of the shift? More generally, perhaps you should look at work of Steffen Roch and his coauthors which has a systematic look at "finite section methods" for approximating operators | |
| Nov 21, 2016 at 20:47 | vote | accept | Anton | ||
| Nov 29, 2016 at 21:04 | |||||
| Nov 21, 2016 at 7:39 | answer | added | Denis Serre | timeline score: 3 | |
| Nov 21, 2016 at 6:39 | answer | added | David Ketcheson | timeline score: 6 | |
| Nov 20, 2016 at 20:21 | comment | added | Christian Remling | Every $|z|<1$ is an eigenvalue with eigenvector $z^n$, so you could just take finitely many of these, truncate them, and make them eigenvectors of a finite-dimensional approximation. It's not so obvious though (to me) if these "approximations" still converge in the strong operator topology; perhaps this will depend on a suitable choice of the eigenvalues. | |
| Nov 19, 2016 at 21:07 | answer | added | T. Amdeberhan | timeline score: 1 | |
| Nov 19, 2016 at 20:11 | comment | added | Anton | I am not sure what topology is suitable for this task, but would like to understand how to find finite-dimensional approximations which do not ignore continuous spectrum. | |
| Nov 19, 2016 at 14:14 | comment | added | David Handelman | Google Berg's method. It's used for approximating the generators of irrational rotation algebras, one of which can be the shift. | |
| Nov 19, 2016 at 14:14 | comment | added | Tomasz Kania | What kind of approximation do you have in mind? Certainly it is not possible in the norm topology. | |
| Nov 19, 2016 at 14:09 | history | asked | Anton | CC BY-SA 3.0 |