论文标题
各向同性拉普拉斯操作员在同质树上的通用性能
Universal properties of the isotropic Laplace operator on homogeneous trees
论文作者
论文摘要
令$ p $为同质树上的各向同性最近的邻居过渡操作员。我们考虑$λ$ - eigenfunctions $ p $ for $λ$以外的$ \ ell^2 $ spectrum，即带有特征的特征函数$γ=λ-laplace operator $ delta = p-delta = p- \ nathbb i $ u $ $ u $ $ uncome $λ-$λ-$λ-$ polyharmormons，该函数是属于$λ- $（delta-γ\ mathbb i）^n $ for $ n \ geqslant 0 $。我们证明，在$λ-$ polyharmonic函数生成的合适的Banach空间上，操作员$ e^{delta-γ\ Mathbb i} $是超循环的，尽管$ delta-γ\ mathbb i $不是。
Let $P$ be the isotropic nearest neighbor transition operator on a homogeneous tree. We consider the $λ$-eigenfunctions of $P$ for $λ$ outside its $\ell^2$ spectrum, i.e., the eigenfunctions with eigenvalue $γ=λ- 1$ of the Laplace operator $Delta=P- \mathbb I$, and also the $λ-$polyharmonic functions, that is, the union of the kernels of $(Delta-γ\mathbb I)^n$ for $n\geqslant 0$. We prove that, on a suitable Banach space generated by the $λ-$polyharmonic functions, the operator $e^{Delta-γ\mathbb I}$ is hypercyclic, although $Delta-γ\mathbb I$ is not.
