Wellposedness of hyperbolic evolution equations in Banach spaces

Well-posedness of non-autonomous linear evolution equations in uniformly convex spaces

This paper addresses the problem of wellposedness of non-autonomous linear evolution equations $\dot x = A(t)x$ in uniformly convex Banach spaces. We assume that $A(t):D \subset X\to X$, for each $t$ is the generator of a quasi-contractive $C_0$-group where the domain $D$ and the growth exponent are independent of $t$. Well-posedness holds provided that $t\mapsto A(t)y$ is Lipschitz for all $y\in D$. Hölder continuity of degree $α<1$ is not sufficient and the assumption of uniform convexity cannot be dropped.

关于Trotter和Zeno乘积公式在玻色子应用中的强界

On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications

本文研究了在Banach空间强算子拓扑下证明Trotter乘积公式与量子Zeno效应定量界的假设条件，通过连续嵌入的Banach空间层级推导了Suzuki高阶界，并展示了其在玻色子应用中的自然实例。

The quest for the ultimate anisotropic Banach space

We present a new scale $U^{t,s}_p$ (with $s<-t<0$ and $1 \le p <\infty$) of anisotropic Banach spaces, defined via Paley-Littlewood, on which the transfer operator associated to a hyperbolic dynamical system has good spectral properties. When $p=1$ and $t$ is an integer, the spaces are analogous to the "geometric" spaces considered by Gouëzel and Liverani. When $p>1$ and $-1+1/p<s<-t<0<t<1/p$, the spaces are somewhat analogous to the geometric spaces considered by Demers and Liverani. In addition, just like for the "microlocal" spaces defined by Baladi-Tsujii, the spaces $U^{t,s}_p$ are amenab…