论文标题
关于双分子和以卷积为主的操作员
On dual molecules and convolution-dominated operators
论文作者
论文摘要
我们表明，可以通过再现其双重系统形成分子的内核来获得复制内核希尔伯特空间中的采样或插值公式，从而确保函数的尺寸曲线被其采样值的大小曲线完全反映。主要工具是用于卷积为主导的算子的局部霍明型微积分，对可能非物质生长的群体有效。应用于组表示的矩阵系数，我们的方法改善了原子分解的经典结果，并弥合了抽象和混凝土方法之间的差距。
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size profile of its sampled values. The main tool is a local holomorphic calculus for convolution-dominated operators, valid for groups with possibly non-polynomial growth. Applied to the matrix coefficients of a group representation, our methods improve on classical results on atomic decompositions and bridge a gap between abstract and concrete methods.
