论文标题
多芯片群空间上的Toeplitz和相关操作员
Toeplitz and related operators on polyanalytic Fock spaces
论文作者
论文摘要
我们从极限运算符方面，将紧凑型和弗雷德尔姆操作员的表征在多个分析的fock空间上进行表征。作为应用程序，我们使用矩阵值Berezin型转换获得了Bauer-Isralowitz定理的概括。然后，我们将此定理应用于Toeplitz和Hankel操作员，以获得紧凑性的必要条件。事实证明，无论是toeplitz还是Hankel操作员都紧凑不取决于多序列顺序。对于Hankel操作员，这甚至包含真正的多状虫水平的空间。
We give a characterization of compact and Fredholm operators on polyanalytic Fock spaces in terms of limit operators. As an application we obtain a generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin type transform. We then apply this theorem to Toeplitz and Hankel operators to obtain necessary and sufficient conditions for compactness. As it turns out, whether or not a Toeplitz or Hankel operator is compact does not depend on the polyanalytic order. For Hankel operators this even holds on the true polyanalytic Fock spaces.
