论文标题
$ l^p $和应用程序的分数傅立叶变换
Fractional Fourier transforms on $L^p$ and applications
论文作者
论文摘要
本文以$ 1 \ le P <2 $为$ l^p（\ mathbb r）$理论。鉴于FRFT的特殊结构，我们通过引入合适的CHIRP操作员来研究$ l^1 $函数的FRFT属性。但是，在$ l^1（\ mathbb {r}）$设置中，即使执行函数的基本操作，也会出现收敛问题。我们克服了此类问题，并通过合适的手段（例如分数高斯和亚伯手段）来研究FRFT反转问题。我们还获得了分数卷积的规律性，并获得了FRFT平均值的侧面收敛结果。最后，我们讨论了$ l^p $乘数结果以及与FRFT相关的Littlewood-Paley定理。
This paper is devoted to the $L^p(\mathbb R)$ theory of the fractional Fourier transform (FRFT) for $1\le p < 2$. In view of the special structure of the FRFT, we study FRFT properties of $L^1$ functions, via the introduction of a suitable chirp operator. However, in the $L^1(\mathbb{R})$ setting, problems of convergence arise even when basic manipulations of functions are performed. We overcome such issues and study the FRFT inversion problem via approximation by suitable means, such as the fractional Gauss and Abel means. We also obtain the regularity of fractional convolution and results on pointwise convergence of FRFT means. Finally we discuss $L^p$ multiplier results and a Littlewood-Paley theorem associated with FRFT.
