Bergman位移的游荡子空间中函数的双圆盘Hardy空间刻画

Characterizations of functions in wandering subspaces of the Bergman shift via the Hardy space of the bidisc

设W为Bergman位移的不变子空间相应的游荡子空间.通过将Bergman空间与双圆盘Hardy空间的商空间H2(D2)Θ[z-w]等同,本文给出了H2(D2)Θ[z-w]的闭子空间为Bergman位移的不变子空间相应的游荡子空间的充要条件,由此给出了Bergman位移的游荡子空间中函数的刻画以及函数的系数刻画.最后,定义了从一个游荡子空间到另一个游荡子空间的算子,并给出了与Bergman位移的万有性质相关的算子分解定理.

Let W be the wandering subspace corresponding to an invariant subspace of the Bergman shift.By identifying the Bergman space with H~2(D~2)Θ[z-w],we give a necessary and sufficient condition for a closed subspace of H~2(D~2)Θ[z-w]to be a wandering subspace of an invariant subspace.Furthermore,we present a functional characterization and a coefficient characterization for a function in a wandering subspace.Finally,we define an operator from one wandering subspace to another,and get a decomposition theorem for such an operator,which is related to the universal property of the Bergman shift.