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5
votes
0answers
160 views
+100

Uniqueness direct sum decomposition representations of quantum group

Let $\mathbb{G}$ be a $C^*$-algebraic compact quantum group with function algebra $(C(\mathbb{G}), \Delta)$. Let $\{X_i \in B(H_i)\otimes C(\mathbb{G})\}_{i \in I}$ be a maximal family of pairwise non-...
4
votes
0answers
119 views
+50

Tensor product of representations on a compact quantum group

Let $\mathbb{G}$ be a $C^*$-algebraic compact quantum group (in the sense of Woronowicz) with function algebra $(C(\mathbb{G}), \Delta)$. Let $X \in M(B_0(H)\otimes C(\mathbb{G}))$ and $Y \in M(B_0(K)\...
5
votes
1answer
157 views
+100

When do volumes depend real-analytically on the parameters defining the regions?

Suppose $f_1, \dots, f_n$ are real-valued real analytic functions defined on an open set $B=(0,1)^d$ of $\mathbb{R}^d$. For $r \in \mathbb{R}$, let $S_r$ be the sub-level set in $B$ defined by the ...
2
votes
0answers
123 views
+50

Generalising Bäcklund tranform to solve $\omega''(t)=t\sin\omega(t)$

Bäcklund tranformations may be used also in ODE to solve non-linear problems; for instance, it's well known that for the equation $$ \begin{align} \frac{\mathrm{d}^2\omega}{\mathrm{d}t^2}=\sin\omega \...
7
votes
0answers
68 views
+50

Do compact inverse-property loops (or just compact Moufang loops) have bi-invariant Haar measure?

So, the overall question is in the title: Does a compact topological loop with the inverse property have a Haar measure that is simultaneously left invariant? (And we can restrict to Moufang loops if ...
12
votes
1answer
373 views
+500

Is there an infinitary sentence which is absolutely not second-order expressible?

This is a "forcing-absolute" followup to this question, whose answer was largely unsatisfying. The question is: Suppose $V=L$. Is there an $\mathcal{L}_{\infty,\omega}$-sentence $\varphi$ ...
4
votes
1answer
158 views
+300

A variant to the Fokker–Planck equation

Consider the PDE of $p(t,x)\ge 0$ given as $$\partial_t p = \frac{\partial^2_{xx}p}{(1+m(t))^2} - \partial_x p,\quad \forall t,~x \in (0,\infty)$$ with initial and boundary conditions $p(0,\cdot)=\rho$...
14
votes
0answers
339 views
+50

From coin flips to algebraic functions via pushdown automata

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...
4
votes
0answers
70 views
+50

Bochner–Minlos Theorem for locally convex spaces and their duals

Let $(X,\tau)$ be a locally convex space and $(X^{*},\tau_{s})$ be its topological dual space equipped with the strong topology. Denote by $S(X,X^{*})$ the collection of operators from $X$ to $X^{*}$ ...
1
vote
0answers
177 views
+50

Collection of proper classes with in CZF

In Aczel's Constructive Set Theory (CZF), no non-degenerate complete lattice can be proved to be a set. There are hallmark examples of complete lattices that are proper classes in CZF, including the ...
3
votes
0answers
153 views
+50

Using the Holtz method to build polynomials that converge to a continuous function

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...