论文标题
统一的乘数光谱特性的方法
Unified approach to spectral properties of multipliers
论文作者
论文摘要
令$ \ mathbb b_n $为$ \ mathbb c^n $中的打开单位球。我们表征了点上的乘数$ m_u $的光谱，该光谱在$ \ mathbb b_n $满足某些一般条件下作用于分析功能的Banach空间。这些空间包括Bergman-Sobolev空间$ a^p_^p_ {α，β} $，bloch型空间$ \ MATHCALB_α$，加权Hardy Spaces $ H^p_w $带有Muckenhoupt重量和Hardy-Sobolev Hilbert Space $ H^2_β$。此外，我们在大多数上述空间中描述了乘数的必要光谱，尤其是在那些乘数集是球代数子集的空间中。
Let $\mathbb B_n$ be the open unit ball in $\mathbb C^n$. We characterize the spectra of pointwise multipliers $M_u$ acting on Banach spaces of analytic functions on $\mathbb B_n$ satisfying some general conditions. These spaces include Bergman-Sobolev spaces $A^p_{α,β}$, Bloch-type spaces $\mathcal B_α$, weighted Hardy spaces $H^p_w$ with Muckenhoupt weights and Hardy-Sobolev Hilbert spaces $H^2_β$. Moreover, we describe the essential spectra of multipliers in most of the aforementioned spaces, in particular, in those spaces for which the set of multipliers is a subset of the ball algebra.
