论文标题
商人域商的伯格曼（Bergman）空间的托管运营商
Toeplitz operators on the weighted Bergman spaces of quotient domains
论文作者
论文摘要
令$ g $为有限的伪反射组，$ω\ subseteq \ mathbb c^d $是一个有限的域，是$ g $ - 空间。我们在加权伯格曼（Bergman）$ω$和$ω$和$ω/g $上使用不变理论和$G。$G。$的代表理论建立了涉及Toeplitz运营商的身份。$G。$又提供了研究toeplitz运营商在$ω/G的加权伯格曼领域的代数性能的代数性能。操作员。结果，在某些特定商域上的加权伯格曼空间上的Toeplitz运算符（即对对称的polydisc，单一多面体，鲁丁的域）上更复杂的结果。
Let $G$ be a finite pseudoreflection group and $Ω\subseteq \mathbb C^d$ be a bounded domain which is a $G$-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of $Ω$ and $Ω/G$ using invariant theory and representation theory of $G.$ This, in turn, provides techniques to study algebraic properties of Toeplitz operators on the weighted Bergman space on $Ω/G.$ We specialize on the generalized zero-product problem and characterization of commuting pairs of Toeplitz operators. As a consequence, more intricate results on Toeplitz operators on the weighted Bergman spaces on some specific quotient domains (namely symmetrized polydisc, monomial polyhedron, Rudin's domain) have been obtained.
