11 problems

Let $\Omega$ be an irreducible symmetric cone, and let $H$ be a self-scaled barrier on $\Omega$. A self-scaled barrier is isotropic when it is rotationally invariant under the rele…

Let $1\leq p,s<\infty$. For some $\mu>0$, let $C_\mu$ be a constant such that, for every $j\geq1$ and every sequence $\{f_k\}$ satisfying…

Let $k\in\mathbb N_0$, let $\Re\mu>\mu_0+kq+1$, and let $\nu\in E_k$. Suppose that the beta distribution $\beta_{\mu,\nu}$ is a complex measure, meaning that…

BBGRS conjecture. The Bergman projector $P_\nu$ admits a bounded extension to $L^p_\nu$ if and only if

Let $D$ be a cross-section of a proper open cone, and let $\operatorname{Isom}(D)$ and $\operatorname{Coll}(D)$ denote respectively the isometry group and the collineation group of…

Let $H_n(\mathbb{R})^+$ denote the cone of real symmetric positive semidefinite $n\times n$ matrices. Let $\mathfrak{s}(C)$ be the cone of generators of one-parameter semigroups of…

Let $C$ be a symmetric cone, and let $B$ be an exotic drift, meaning an inward-pointing drift constructed in the paper that cannot be written as a sum of a Lie algebra element and…

Let $C\subseteq V$ be a symmetric cone. A linear map $B:V\to V$ is inward-pointing when … for all $u,v\in C$ satisfying $\langle u,v\rangle=0$. A Lie algebra element is a generator…

Symmetric-cone conjecture. The groups $\mathrm{Isom}(X)$ and $\mathrm{Coll}(X)$ differ if and only if the cone generated by $X$ is symmetric and not Lorentzian. In that case, the i…

Let $T_\Omega$ be a tube domain over an irreducible symmetric cone, let $\mathbb{B}^p_\nu(T_\Omega)$ be the analytic Besov space defined using $\Delta^k(\operatorname{Im}z)\Box^kF$…

Let $T_\Omega=\mathbb{R}^n+i\Omega$ be a tube domain over an irreducible symmetric cone $\Omega\subset\mathbb{R}^n$ of rank $r$, with determinant function $\Delta$, and let ……