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2021.12.8,傅尊伟,教授,临沂大学,Riesz transform associated with the fractional Fourier transform and applications

报告题目Riesz transform associated with the fractional Fourier transform and applications

报告人:傅尊伟教授  临沂大学

报告人简介

傅尊伟,博士、教授,中韩大数据与人工智能研究中心主任;临沂大学数学与统计学院院长;水原大学博士生导师;山东师范大学博士生导师。山东省特级教师工作坊主持人,山东省大数据专业建设委员会副主任委员。山东省应用数学重点学科首席专家。山东省五一劳动奖章获得者、全省教育先进工作者; 香港求是研究生奖学金获得者; 全国优秀教师。

傅尊伟教授在《IEEE TNNLS》、《IEEE TFS》、《ACHA》、《JDE》、《Information Sci.》和《中国科学》等学术杂志上发表论文若干。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。先后主持国家自然科学基金4(青年1项、面上3)。国家一流课程《数学分析》主讲教师。IEEE会员,美国《数学评论》评论员。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。

报告时间20211281930

腾讯会议766 944 950

报告摘要Since Zayed [30, Zayed, 1998] introduced the fractional Hilbert transform related to the fractional Fourier transform, this transform has been widely concerned and ap- plied in the field of signal processing. Recently, Chen, the first, second and fourth authors [6, Chen et al, 2021] attribute it to the operator corresponding to fractional multiplier, but it is only limited to 1-dimensional case. This paper naturally considers the high-dimensional situation. We introduce the fractional Riesz transform associated with fractional Fourier transform, in which the chirp function is the key factor and the technical barriers to be overcome. Furthermore, after equipping with chirp functions, we introduce and investigate the boundedness of singular integral operators, the dual properties of Hardy spaces and BMO spaces as well as the applications of theory of fractional multiplier in partial differential equation, which completely matched some classical results. Through numerical simulation, we give the physical and geometric interpretation of the high-dimensional fractional multiplier theorem. Finally, we present the application of the fractional Riesz transform in edge detection, which verifies the prediction proposed in [26, Xu et al, 2016]. Moreover, the application presented in this paper can also be considered as the high-dimensional case of the application of the continuous fractional Hilbert transform in edge detection in [23, Pei and Yeh, 2000]. This is joint work with Prof. Grafakos, Prof. Lin, Prof. Wu and Dr. Yang.