论文标题
操作员的时频分析和库里特空间
Time-Frequency Analysis and Coorbit Spaces of Operators
论文作者
论文摘要
我们为带有操作员窗口的某些类别的操作员介绍了一个有价值的短时傅立叶变换，并表明转换以一种类似的方式来实现短期傅立叶变换的功能，特别是引起了一个矢量价值繁殖的载体banach Space的家族，即所谓的COORBIT空间，作为操作员的空间。由于这种结构，运算符在功能调制空间上生成等效规范的操作员已完全分类。我们表明，这些操作员空间具有与函数空间相同的原子分解属性，并使用它来使用本地化操作员对空间进行表征。
We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular giving rise to a family of vector-valued reproducing kernel Banach spaces, the so called coorbit spaces, as spaces of operators. As a result of this structure the operators generating equivalent norms on the function modulation spaces are fully classified. We show that these operator spaces have the same atomic decomposition properties as the function spaces, and use this to give a characterisation of the spaces using localisation operators.
