Timeline for Does the sequence of bounded symmetric square integrable holomorphic functions have a convergent subsequence?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| S Jun 30 at 9:04 | history | bounty ended | CommunityBot | ||
| S Jun 30 at 9:04 | history | notice removed | CommunityBot | ||
| Jun 25 at 9:07 | comment | added | Anacardium | @VítTuček$:$ Exactly! You have rightly pointed it out. The Bergman space is decomposed into the orthogonal direct sum of its symmetric and anti-symmetric part. Sorry for the late reply. | |
| Jun 24 at 18:17 | comment | added | Vít Tuček | So, strictly speaking, no anti-symmetric functions are not the set theoretic complement of the symmetric functions. :) But I think that there is orthogonal decomposition of $L^2(\mathbb{D})$ into symmetric and anti-symmetric functions (sending $f$ to the pair $(1/2[f(a,b) + f(b,a)], 1/2[f(a,b)-f(b,a)]$). Is that your setting? | |
| Jun 24 at 5:05 | comment | added | Anacardium | @VítTuček$:$ Yes. More precisely $f$ Is anti-symmetric on $\mathbb D^2$ if $f(z_1,z_2) = - f(z_2,z_1),$ for all $(z_1,z_2) \in \mathbb D^2.$ | |
| Jun 23 at 22:40 | comment | added | Vít Tuček | So anti-symmetric functions are all those which are not symmetric? | |
| Jun 23 at 6:05 | comment | added | Anacardium | @VítTuček$:$ Symmetric functions are those which are invariant under the $S_2$-action on $\mathbb A^2 \left (\mathbb D^2 \right)$ and anti-symmetric functions are those that are altered according to the permutations of $S_2.$ | |
| Jun 22 at 21:45 | comment | added | Vít Tuček | Please define symmetric and anti-symmetric functions. | |
| S Jun 22 at 7:16 | history | bounty started | Anacardium | ||
| S Jun 22 at 7:16 | history | notice added | Anacardium | Authoritative reference needed | |
| Jun 15 at 20:45 | history | asked | Anacardium | CC BY-SA 4.0 |