5 problems

$SU(2,2)$ coherent-state basis conjecture. The set $\{\psi_{r,s}^{\ell,m}:\ell,m,r,s\in\mathbb{N}\}$ forms an orthonormal basis of $F_{2,2,n}^{U(n)}$. The formulas have been checke…

Let ${\mathcal F}_j$ be the spin-$j$ function space, let $\lVert\cdot\rVert_2$ be the normalized norm, and let … be the Wehrl entropy of an $f\in{\mathcal F}_j$ normalized by…

Let ${\mathcal F}_j$ be the spin-$j$ function space on ${\mathbb S}^2={\mathbb C}\cup\{\infty\}$, and for $p\geq 1$ define the normalized norm by … Let $K(z,w)$ denote the coherent…

Fix $\alpha>0$ and $s\geq1$. Let $U$ be the affine-group representation on $L^2(\mathbb{R}_+)$, let $\eta_\alpha(k)=C(\alpha)k^\alpha e^{-k}$, and define…

Resolution-of-unity conjecture. For sufficiently small $t>0$, the displayed resolution of unity and the stated asymptotic scaling of $C_t$ hold for an arbitrary Lie group $G$. If…