论文标题
在均匀分解空间的离散转换上
On a discrete transform of homogeneous decomposition spaces
论文作者
论文摘要
我们在（各向异性）离散的均匀型三角形型型型空间和均质调制空间中引入了几乎对角线矩阵，并且显示出在矩阵乘法下封闭的几乎几乎对角线矩阵的类别。 然后，我们将结果连接到连续设置，并表明具有合适衰减属性的一对时频帧的“帧更改”矩阵几乎是对角线的。作为此结果的应用，我们考虑了Triebel-Lizorkin类型和相关调制空间的均质分解空间的紧凑型框架扩展的构造。
We introduce almost diagonal matrices in the setting of (anisotropic) discrete homogeneous Triebel-Lizorkin type spaces and homogeneous modulation spaces, and it is shown that the class of almost diagonal matrices is closed under matrix multiplication. We then connect the results to the continuous setting and show that the "change of frame" matrix for a pair of time-frequency frames, with suitable decay properties, is almost diagonal. As an application of this result, we consider a construction of compactly supported frame expansions for homogeneous decomposition spaces of Triebel-Lizorkin type and for the associated modulation spaces.
