论文标题
关于全态函数半群的光谱值
On the spectral value of Semigroups of Holomorphic Functions
论文作者
论文摘要
令$（ϕ_t）_ {t \ geq 0} $是单位磁盘$ \ mathbb {d} $的单态自图的半群，带有denjoy-wolff point $τ= 1 $。角导数为$ ϕ_t^{\ prime}（1）= e^{ - λt} $，其中$λ\ geq 0 $是$（ϕ_t）$的频谱值。如果$λ> 0 $ semigroup是双曲线，否则是抛物线。假设$ k $是$ \ mathbb {d} $的紧凑型非极性子集，具有正对数能力。我们通过检查$ ϕ_t（k）$的渐近行为来指定半群的类型。我们通过使用几种潜在理论量（例如谐波测量，绿色功能，极长，冷凝器容量。
Let $(ϕ_t)_{t \geq 0}$ be a semigroup of holomorphic self-maps of the unit disk $\mathbb{D}$ with Denjoy-Wolff point $τ=1$. The angular derivative is $ϕ_t^{\prime}(1)= e^{-λt}$, where $λ\geq 0$ is the spectral value of $(ϕ_t)$. If $λ>0$ the semigroup is hyperbolic, otherwise it is parabolic. Suppose $K$ is a compact non-polar subset of $\mathbb{D}$ with positive logarithmic capacity. We specify the type of the semigroup by examining the asymptotic behavior of $ϕ_t(K)$. We provide a representation of the spectral value of the semigroup with the use of several potential theoretic quantities e.g. harmonic measure, Green function, extremal length, condenser capacity.
