论文标题
$ l^2（\ mathbb r）$中的分数生物表达小波
Fractional Biorthogonal wavelets in $L^2(\mathbb R)$
论文作者
论文摘要
这是傅立叶变换的概括（FRFT）的分数傅立叶变换（FRFT），由于其在电气工程和光学元件中的应用，近年来已成为许多研究论文的重点。在本文中，我们在$ \ mathbb {r} $上介绍了分数生物三相的概念，并为单个函数的翻译获得了必要和足够的条件，以形成封闭线性跨度的分数riesz碱基。我们还为两个分数MRA和相关的分数生物表定小波家族的分数缩放函数翻译的分数生物三相合并性提供了完整的表征。此外，在对分数缩放函数和相应的分数小波的轻度假设下，我们表明分数小波可以生成$ l^2（\ Mathbb r）的reisz碱基。$。
The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we introduce the notion of fractional biorthogonal wavelets on $\mathbb{R}$ and obtain the necessary and sufficient conditions for the translates of a single function to form the fractional Riesz bases for their closed linear span. We also provide a complete characterization for the fractional biorthogonality of the translates of fractional scaling functions of two fractional MRAs and the associated fractional biorthogonal wavelet families. Moreover, under mild assumptions on the fractional scaling functions and the corresponding fractional wavelets, we show that the fractional wavelets can generate Reisz bases for $L^2(\mathbb R).$.
