6 problems

Coefficient ratio conjecture. Then

Let $\Omega$ be a bounded symmetric domain of rank $r$, with invariants $p$, $b$, $d$, and $q_\Omega$, and let $\Gamma_\Omega$ denote the associated gamma function. Let $m$ and…

Let $D$ be a bounded planar domain with analytic boundary and connectivity $n>1$. For $z e w$ in $D$, let $GD(w,z)$ be the Green function and define the logarithmic capacity by … L…

Let $D$ be a planar regular region whose boundary consists of $n$ analytic Jordan curves. Let $\hat{R}(z,\bar{w})$ be its conjugate Hardy $H^{2}$ kernel and $B(z,\bar{w})$ its Berg…

Atomicity conjecture. If $R(\Phi)<\infty$, then $(X,\mu)$ is atomic.

A-F-M conjecture. The multiplication operator $M_z$ on $\mathcal H(K_1+K_2)$ is subnormal.