论文标题
$ l^2（\ mathbb r）$中的分数多解决分析和相关缩放函数
Fractional Multiresolution Analysis and Associated Scaling Functions in $L^2(\mathbb R)$
论文作者
论文摘要
在本文中，我们通过假设分数在分数多分析分析的核心子空间中构成单个函数的分数构成riesz基础而不是正顺序基础，从而展示了如何从riesz基础构建正统基础。在分数多分析分析的定义中，我们表明交叉点琐碎条件来自其他条件。此外，我们表明联合密度条件还遵循以下假设：缩放函数的分数傅立叶变换连续$ 0 $。在高潮时，我们提供了与分数多溶剂分析相关的缩放函数的完整表征。
In this paper, we show how to construct an orthonormal basis from Riesz basis by assuming that the fractional translates of a single function in the core subspace of the fractional multiresolution analysis form a Riesz basis instead of an orthonormal basis. In the definition of fractional multiresolution analysis, we show that the intersection triviality condition follows from the other conditions. Furthermore, we show that the union density condition also follows under the assumption that the fractional Fourier transform of the scaling function is continuous at $0$. At the culmination, we provide the complete characterization of the scaling functions associated with fractional multiresolutrion analysis.
