中国矿业大学（北京）tyc1286太阳成集团

学术报告

时间：2019年11月11日（星期一）下午3:30-4:30

地点：逸夫实验楼1417

报告题目：Fractional Fourier transforms on $L^p$ and applications报告题目：Fractional Fourier transforms on $L^p$  and applications
报告摘要：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.  Furthermore, we discuss  $L^p$ multiplier results and a Littlewood-Paley theorem associated with FRFT.  In the last section, using the language of time-frequency analysis, this means that an L1 chirp signal, whose FRFT is non-integrable, is recovered from the frequency domain as a limit of the inverted Abel means of its FRFT . This is the joint work with Dr. Wei Chen, Prof. Grafakos Loukas and Dr. Yue Wu.

祝好！

尊伟」
—————————报告题目：Fractional Fourier transforms on $L^p$  and applications
报告摘要：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.  Furthermore, we discuss  $L^p$ multiplier results and a Littlewood-Paley theorem associated with FRFT.  In the last section, using the language of time-frequency analysis, this means that an L1 chirp signal, whose FRFT is non-integrable, is recovered from the frequency domain as a limit of the inverted Abel means of its FRFT . This is the joint work with Dr. Wei Chen, Prof. Grafakos Loukas and Dr. Yue Wu.

祝好！

尊伟」
—————————报告题目：Fractional Fourier transforms on $L^p$  and applications
报告摘要：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.  Furthermore, we discuss  $L^p$ multiplier results and a Littlewood-Paley theorem associated with FRFT.  In the last section, using the language of time-frequency analysis, this means that an L1 chirp signal, whose FRFT is non-integrable, is recovered from the frequency domain as a limit of the inverted Abel means of its FRFT . This is the joint work with Dr. Wei Chen, Prof. Grafakos Loukas and Dr. Yue Wu.

祝好！

尊伟」
—————————

报告人：傅尊伟教授 临沂大学

报告摘要： In this talk, we study 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. Furthermore, we discuss $L^p$ multiplier results and a Littlewood-Paley theorem associated with FRFT.  In the last section, using the language of time-frequency analysis, this means that an L1 chirp signal, whose FRFT is non-integrable, is recovered from the frequency domain as a limit of the inverted Abel means of its FRFT. This is the joint work with Dr. Wei Chen, Prof. Grafakos Loukas and Dr. Yue Wu.

报告人简介：傅尊伟，博士、教授，临沂大学数学与统计学院院长，韩国水原大学博士生导师。山东省“应用数学”重点学科首席专家、山东省“富民兴鲁”劳动奖章获得者、全省教育先进工作者；“求是”研究生奖学金获得者；全国优秀教师。在《IEEE Trans.》、《J. Differential Equations》、《Appl. Intelligence》、《Proc. Amer. Math. Soc.》和《中国科学》等SCI杂志上发表论文67篇。主持国家自然科学基金青年项目1项、面上项目2项。获得山东省高校优秀科研成果奖一等奖、山东省高等教育教学成果奖一等奖各1项。曾应邀在英国剑桥大学举行的“第二届世界青年数学家大会”上做45分钟学术报告。