Timeline for Is there a meaningful interpretation of an $L^i$-space?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2023 at 2:33 | comment | added | Daniel Asimov | If there are some things about the L^p spaces that vary real-analytically with p, then one pathway might be first to analytically continue those things to a complex neighbourhood of (0,oo), and then to infer from that how the p in L^p might be non-real. [Written before reading the answer by Dmitri Pavlov.] | |
| Jun 16, 2023 at 23:43 | vote | accept | TheSimpliFire | ||
| Jun 16, 2023 at 19:44 | answer | added | Dmitri Pavlov | timeline score: 8 | |
| Jun 16, 2023 at 19:33 | comment | added | Zach Teitler | Perhaps it makes sense to start with Hölder's inequality. What would it say for complex $p,q$ and some simple functions? | |
| Jun 16, 2023 at 19:24 | comment | added | paul garrett | For what it's worth, I can confirm that I myself have absolutely never seen a literal complex-indexed "norm"... | |
| Jun 16, 2023 at 19:23 | comment | added | TheSimpliFire | @paulgarrett It's probably not the best word choice, but I am interested in extending the norm to a complex index. Also, that was just one variant we considered. I did a fair bit of searching but was unable to find anything on this topic. | |
| Jun 16, 2023 at 19:08 | comment | added | paul garrett | Since you mention "spin": is it possible that you're not necessarily/exactly wanting a "norm" with complex index, but, rather, computing a (Fourier-like) component with respect to a (compact?) group action? | |
| Jun 16, 2023 at 17:58 | history | asked | TheSimpliFire | CC BY-SA 4.0 |