论文标题
分析性M层表和加权差异型空间
Analytic m-isometries and weighted Dirichlet-type spaces
论文作者
论文摘要
对应于单位圆圈上任何$（M-1）$ - 元素元素的元素，引入并研究了加权的dirichlet型空间。我们证明，通过坐标函数在这些加权dirichlet型空间上乘法的运算符充当分析性$ m $ ismemetry，并满足某些操作员的不平等。此外，结果表明，满足这组运算符不平等的分析$ m $ iSometry可以用坐标函数在$（M-1）$ - 单位圆圈的半光谱测量值中引起的加权dirichlet-type空间来表示乘法的乘法运算符。这扩展了Richter和Olofsson的结果，分析$ 2 $ isotries。我们还证明，所有左可逆$ m $ concave操作员都满足上述操作员不平等现象都允许wold型分解。该结果是我们模型定理的关键要素，并且还概括了Shimorin在一类$ 3 $ CONCAVE运营商上的结果。
Corresponding to any $(m-1)$-tuple of semi-spectral measures on the unit circle, a weighted Dirichlet-type space is introduced and studied. We prove that the operator of multiplication by the coordinate function on these weighted Dirichlet-type spaces acts as an analytic $m$-isometry and satisfies a certain set of operator inequalities. Moreover, it is shown that an analytic $m$-isometry which satisfies this set of operator inequalities can be represented as an operator of multiplication by the coordinate function on a weighted Dirichlet-type space induced from an $(m-1)$-tuple of semi-spectral measures on the unit circle. This extends a result of Richter as well as of Olofsson on the class of analytic $2$-isometries. We also prove that all left invertible $m$-concave operators satisfying the aforementioned operator inequalities admit a Wold-type decomposition. This result serves as a key ingredient to our model theorem and also generalizes a result of Shimorin on a class of $3$-concave operators.
