开半轴上带标量型谱算子的抽象发展方程弱解的Gevrey超可微性

具有标量型谱算子的抽象发展方程弱解的Gevrey超可微性

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator

发现的条件的标量型谱算子$A$在一个复杂的巴拿赫空间的发展方程\begin{equation*} y'(t)=Ay(t),\ t\ge 0, \end{equation*}的所有弱解的必要和充分的强Gevrey超可微的顺序$β\ge 1$，特别是分析或整个，$[0,\infty)$。某些固有的平滑度改善效果进行了分析。

具有小于1阶标量型谱算子的抽象发展方程弱解的Gevrey超可微性

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one

证明了复巴拿赫空间中具有标量型谱算子$A$的发展方程\begin{equation*} y'(t)=Ay(t),\ t\ge0, \end{equation*}的弱解是阶小于1的Gevrey超可微的，则算子$A$必然有界.

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis

Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\in \mathbb{R}, \] with a scalar type spectral operator $A$ in a complex Banach space, we find conditions on $A$, formulated exclusively in terms of the location of its spectrum in the complex plane, necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly Gevrey ultradifferentiable of order $β\ge 1$, in particular analytic or entire, on $\mathbb{R}$. We also reveal certain inherent smoothness improvement effects and show that, if all weak solutions of the equation…

关于标量型谱算子生成Beurling型Carleman超可微$C_0$ -半群

On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators

建立了Beurling型Carleman超可微$C_0$ -半群的标量型谱生成元的一个刻划，详细地考虑了Gevrey超可微的重要情形，观察了对应于某个快速增长定义序列的一般判据的实现.

On the regularity of scalar type spectral $C_0$-semigroups

We show that, for the $C_0$-semigroups of scalar type spectral operators, a well-known necessary condition for the generation of eventually norm-continuous $C_0$-semigroups, formulated exclusively in terms of the location of the spectrum of the semigroup's generator in the complex plane, is also sufficient and, in fact, characterizes the generators of immediately norm-continuous such semigroups. Combining characterizations of the immediate differentiability and the Gevrey ultradifferentiability of scalar type spectral $C_0$-semigroups with the generation theorem, found earlier by the author, w…