7 problems

Failure conjecture. The family of approximating Hamiltonians will not yield the sought approximation when $a(\epsilon)\sim\epsilon^{\nu}$ with $\nu>1$. In this regime the three pot…

Let $\vb{M}$ be a rotationally invariant random matrix of size $N$ with a non-pathological limiting spectral density. For $z$ outside the spectrum of $\vb{M}$, define … Let…

Resolvent starlikeness conjecture. Every mapping $G_\lambda$ is starlike of order at least $\frac12$. Furthermore, the order of starlikeness of $G_\lambda$ tends to $1$ as…

Fix $s\in\mathbb{R}_{+}$, $x\in\mathbb{R}_{+}$, and define $\tau^{-,j}_{\ell}(s,x)$ as the successive downcrossing times of $[x-\ell,x+\ell]$ by $\varphi(s)$. Let…

Let $K$ be an abstract Klein-Gordon operator on $L^2(\mathbb{R},\mathcal K)$, and let $R_z(t,s)$ and $\mathcal Z_{\pm,z}^{(\pm)}(t)$ be the evolution and asymptotic subspaces defin…

Let $K$ be an abstract Klein-Gordon operator on $L^2(\mathbb{R},\mathcal K)$, and suppose it is asymptotically stationary and stable, with the additional conditions imposed in the…

Let $I=\mathbb{R}$ and let $K$ be an abstract Klein-Gordon operator acting on $L^2(\mathbb{R},\mathcal K)$, with Feynman and anti-Feynman inverses defined for the asymptotically st…