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...
Many tags have synonyms. My understanding is that there are "primary" tags with one or more synonyms. If somebody uses a synonym, then the this tag is automatically replaced by the primary tag. "Synonym" tags should not occur in the tag list at the bottom of a question, but they are searchable. F...
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...
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