6 problems

Let $d$ denote the spatial dimension, and consider quasilinear Klein–Gordon equations with smooth, small initial data, without assuming that the data are localized. The lifespan is…

The Klein–Gordon local smoothing conjecture. The frequency-localized estimate

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…

Let $I=]t_-,t_+[$ or $I=\mathbb{R}$, let $\mathcal K$ be a Hilbert space, and let $K$ be an abstract Klein-Gordon operator of the form … acting on $L^2(I,\mathcal K)$. In the case…