Calderon-Vaillancourt theorem states that any quantization of a bounded symbol (in the sense of this article for example) is a bounded operator on the $L^2(\mathbb{R^n})$ space. I was wondering if there was any way of going back from a $L^2(\mathbb{R^n})-$bounded pseudo-differential operator to o...

The list of tag synonyms contains a column called "created". Does this column contain the date when a synonym was proposed or the date when the synonym was approved? For example, on Mathematics Stack Exchange the tag (holomorphic-functions) is a synonym of complex analysis. When I check the list...

It is what the label promises, the creationdate of the synonym and that is the date the synonym got proposed. Here is how I reach that conclusion: Lets look at the list, specially the synonym for total-reputation. I picked that one because it was created by a non-diamond. Now look at this S...

Say Tag 1 has been added as a synonym of Tag 2, so that new questions attempting to use Tag 1 will be automatically pointed to Tag 2. However, the two tags haven't been merged (yet). Then, if you click on Tag 1 or attempt to search for it, you'll automatically be redirected to the tag page for Ta...

Let $M$ be a smooth closed manifold, $E$ a Hermitian vector bundle over $M$ and $P$ a pseudodifferential operator. Let $u\in D’(M,E)$ such that $Pu=0$. I want show that $$ WF(u) \subset T_0^{*}M \setminus \ell(P),$$ with $\ell(P)$ the set of elliptic points of $P$. The thing is that I know that ...

Calderon-Vaillancourt theorem states that any quantization of a bounded symbol (in the sense of this article for example) is a bounded operator on the $L^2(\mathbb{R^n})$ space. I was wondering if there was any way of going back from a $L^2(\mathbb{R^n})-$bounded pseudo-differential operator to o...

What does the notation: $$O_{\mathcal{S}'\rightarrow \mathcal{S}}(h^\infty)$$ mean in Zworski's semiclassical analysis? (To be clear, I know what $O(h^\infty)$ means in the context of normed and semi-normed spaces.)

I'm working on a linear stability analysis and have reached a quadratic that led me to two eigenvalues of opposite signs. $$\chi s^2 + \bigg [\frac{\chi v^\infty}{d_c} - \frac{\chi\beta}{\zeta} - k + \frac{\tau_c (A_0-A_f^{ss})}{d_c} \bigg ]s + \frac{\beta k}{\zeta}- \frac{k v^\infty}{d_c}$$ Plug...

Let $X_1$ and $X_2$ be i.i.d. random variables from a distribution $D$ on the real numbers with finite variance (and therefore finite mean). Assume that the probability of $X_i = 0$ is $0$. Must it be true that $$ \mathbb{E}\left[ \frac{X_1 X_2}{X_1^2 + X_2^2} \right] \ge 0? $$ If not, what is th...

For the case where some integer, $n$ is coprime to a prime modulus, $p$, I have proven and understood Fermat's Little Theorem as it is nothing more than Euler's Theorem applied to a prime modulus. For the case where some integer $n$ is not coprime to $p$ $$ \gcd(n,p) \neq 1 \implies p | n $$ Th...

In relation to an ongoing election, this post was mentioned: Include information about elections in the newsletter. One of the tags on that question is newsletter, which is a synonym of community-digests. I have noticed that: Searching for [election] "cast your vote" shows this question among th...

The question here seems to be tagged with close, which, last I checked, is a synonym of vote-to-close. How is it possible that a question can be tagged with a synonym? Don't synonyms automatically get replaced on questions?

Creating a synonym does not ever cause an automatic merging of the questions. All it does is remap future occurrences of the tag to the master tag. When I created that synonym relationship, I didn't bother merging them for whatever reason. That means any questions that were already tagged with c...

For example, on the Physics SE, the [biology] tag exists as both. Here is the SEDE query to the tag, and to the synonym.

A tag could be set on a post (or many posts) well before it becomes a synonym. Once a such tag does become a synonym, we do not go and edit all posts with it in order to change it to its synonym - if someone happens to edit it, that will automatically happen, but if no one does, it will not. Th...

This is a followup of Gilles' comment here. As as result of https://meta.stackexchange.com/questions/128315/the-great-stack-overflow-tag-question-cleanup-of-2012, a lot of questions were being retagged. I'll focus on the assembly tag, but I suppose the problem applies to other tags as well. O...

Possible Duplicate: Remapping of some tag synonyms is broken See this question, and its revision history, which until just now was tagged switch even though that tag is a synonym for switch-statement. I just edited the question, however, I made absolutely no changes to anything. My ed...

mysql has the following synonyms: my-sql and mysql-query. However, mysql-query seems to still have its own life, questions and followers. Shouldn't the entire tag and its questions and followers be merged into mysql since it's a synonym? Update: interesting, for java the last two synonyms java...

This just means the tags need to be merged at some point. It's not a bug.

Regarding, mysql-query & java-api, synonyms process is done by community votes. (batch merging can be done by moderators only, so it moderator didn't involve the tag synonyms process, they won't notice they need to do merging for those tags, right away, isn't it?) New questions will be automa...