论文标题
由laplacian在同质树上的分析功能产生的半群的动力学
Dynamics of semigroups generated by analytic functions of the Laplacian on Homogeneous Trees
论文作者
论文摘要
令$ f $为一个非恒定复合物值分析函数，该功能在包含Laplacian $ \ Mathcal l $的$ l^p $ -spectrum上定义的，在同质树上。在本文中，我们为Semigroup $ t（t）= e^{tf（\ Mathcal {l}）} $提供了必要和充分的条件，以使$ l^{p} $ - 空格混乱。我们还研究了分别研究Semigroup $ t（t）= e^{t（a \ Mathcal {l}+b）} $的混乱动力学，并获得$ t（t）$在$ l^{p} $ space上混乱的$ b $的清晰范围。它包括一些重要的半群，例如热半群和Schrödinger半群。
Let $f$ be a non-constant complex-valued analytic function defined on a connected, open set containing the $L^p$-spectrum of the Laplacian $\mathcal L$ on a homogeneous tree. In this paper we give a necessary and sufficient condition for the semigroup $T(t)=e^{tf(\mathcal{L})}$ to be chaotic on $L^{p}$-spaces. We also study the chaotic dynamics of the semigroup $T(t)=e^{t(a\mathcal{L}+b)}$ separately and obtain the sharp range of $b$ for which $T(t)$ is chaotic on $L^{p}$-spaces. It includes some of the important semigroups, such as the heat semigroup and the Schrödinger semigroup.
