Definition talk:Zero-Limit Sequence in Schwartz Space

I repeat my plea: you can source your "corrections", can you?

I understand that the original page was sourced directly from the Sasane work. Unless Sasane doesn't know what he's talking about, and is actually wrong, it is suboptimal to just change it because you know better.

So please don't just change stuff like this, even though everybody knows you're by far the cleverest person here, without first reviewing the source from which the "incorrect" version is printed, because it might just be the case that what is there is a simplified entry-level version of the definition which is used for lesser mortals who are struggling with this material at first sight. --prime mover (talk) 20:42, 24 October 2022 (UTC)


 * Looking at it more closely, it seems that the original was not "incorrect", but a special case of the more general form that you expanded it to. However, such is not how the Sasane work presented it, and this has resulted in the source citation no longer being accurate. I suggest and recommend that the more general version be presented separately, while the specific version where the limit is $\bszero$ should subpage it. --prime mover (talk) 20:58, 24 October 2022 (UTC)


 * I thought I just corrected an obvious mistake, since:
 * $\paren 1$: The page is named Definition:Convergent Sequence/Schwartz Space but the convergent sequence was not defined, instead only zero sequence.
 * $\paren 2$: The assumption "Let $\phi \in \map \SS \R$ be a Schwartz test function" was there, but $\phi$ was nowhere used.
 * If you want to revert my correction, then pleas rename this pate to Definition:Zero Sequence/Schwartz Space and delete the assumption of $\phi$.--Usagiop (talk) 21:33, 24 October 2022 (UTC)
 * But I will ask for checking the source beforehand.--Usagiop (talk) 21:43, 24 October 2022 (UTC)


 * I agree that the title should be changed. For Schwartz spaces general convergence is not discussed - only the convergence to $\mathbf 0$ is provided. This is done because distributions are linear, so one can incorporate the limit into the sequence itself and solve a modified problem without loss of generality. Indeed $\phi$ here is not being used here and can be removed. Fixing the rest of the content of the page is suboptimal - there are pages linked to this one resting on convergence to $\mathbf 0$. Please revert to the previous version. You are free to rename the original page according to your taste.--Julius (talk) 23:11, 24 October 2022 (UTC)
 * I've reverted it, Julius -- please feel to determine what the name of this page now needs to be. --prime mover (talk) 05:09, 25 October 2022 (UTC)
 * Once the dust has settled, a page explaining and proving the above paragraph would then be essential to remove the confusion that this talk page exemplifies. --prime mover (talk) 05:09, 25 October 2022 (UTC)
 * Let me note that convergence to $\mathbf 0$ is just a special case of the general convergence. Not a real issue. But feel free to revert it as you like. --Usagiop (talk) 00:52, 25 October 2022 (UTC)
 * But if you revert and rename this page, you still need a page for the definition of $\phi_n \stackrel \SS {\longrightarrow} \phi$ which looks exactly like this. --Usagiop (talk) 01:01, 25 October 2022 (UTC)
 * You're the one who wants it, so feel free to create it. --prime mover (talk) 05:07, 25 October 2022 (UTC)


 * For now we should keep this page as it is unless two things are done. Firstly, we need a definition page for a general convergent sequence. Secondly, we need to prove that, thanks to linearity of tempered distributions, $\phi_n \stackrel \SS {\longrightarrow} \phi$ iff $\phi_n - \phi \stackrel \SS {\longrightarrow} 0$. If we had these two pages, then this one could be simplified considerably by defining it as a convergent sequence with limit zero. I think we should still keep this definition in this or a simplified form, because in certain contexts it reduces the notational load. As for the title, we already have Definition:Space of Zero-Limit Sequences, so we could use Zero-Limit Sequence/Schwartz Space.--Julius (talk) 07:48, 25 October 2022 (UTC)