论文标题
大约倾斜双帧
Approximate oblique dual frames
论文作者
论文摘要
在使用框架的表示中，在必须在不同子空间中进行分析和合成的情况下，倾斜二元性出现。在某些情况下，我们无法获得斜双与双重表达的明确表达，而在其他情况下，只有一个倾斜的双框架，而没有我们需要的属性。同样，实际上，计算不是精确的。为了解决这些问题，在这项工作中，我们首先在可分离的希尔伯特空间中介绍并研究了近似倾斜双帧的概念。我们提出了几种属性，并提供了近似倾斜双帧的不同特征。然后，我们将重点放在l^2（r）的移位不变子空间中的近似倾斜双帧以及确保其存在的发电机上的不同条件上。用B-Splines生成的帧序列的示例说明了从数值和计算观点中近似倾斜的双帧的重要性，在该帧序列中，先前的结果用于构造比确切属性更好的属性的近似倾斜双帧。我们为近似误差提供了一种表达方式，并研究其行为。
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others there exists only one oblique dual frame which has not the properties we need. Also, in practice the computations are not exact. To give a solution to these problems, in this work we introduce and investigate the notion of approximate oblique dual frames first in the setting of separable Hilbert spaces. We present several properties and provide different characterizations of approximate oblique dual frames. We focus then on approximate oblique dual frames in shift-invariant subspaces of L^2(R)and g ive different conditions on the generators that assure their existence. The importance of approximate oblique dual frames from a numerical and computational point of view is illustrated with an example of frame sequences generated by B-splines, where the previous results are used to construct approximate oblique dual frames which have better attributes than the exact ones. We provide an expression for the approximation error and study its behaviour.
