一、报告题目：应用调和分析中若干问题

二、报告人：孙颀彧教授
三、时间：2016年12月22日下午14:00---16:00

12月23日上午9:00--11:00

12月23日下午14:00--16:00

四、地点：闻理园A4-305室

五、报告摘要：

Lecture I : Wiener’s lemma and spectral invariance
Wiener’s lemma states that a periodic function with absolutely convergent Fourier series has its reciprocal with absolutely convergent Fourier series if it does not vanish on the real line. The above lemma has applications from pure mathematics, applied mathematics and electronic engineering. The Wiener’s lemma was extended to noncommutative Banach algebras and infinite matrices. In this lecture, I will introduce three different approaches, including localization technique, spectral approach and commutator estimates. Also I will discuss several applications to spectral invariance of Bochner-Reisz means and Bessel potentials, localized inverse functions, and sparse optimizations.
Lecture 2: Compressive sensing
Compressive sensing is a signal processing technique for efficiently acquiring and reconstructing a signal by finding underdetermined linear systems. It is based on the principle that sparse signal can be recovered from its samples from far few samples than required by the Byquist rate. In this lecture, I will introduce the optimization approach to solve compressive sensing problems, and discuss null space property and restricted isometry property.
Lecture 3: Phase retrieval
Phase retrieval arises in various fields of science and engineering. Phase retrieval plays important roles in signal/image/speech processing. It consists of reconstructing a signal of interest from its magnitude measurements. In this lecture, I will consider phase retrieval problem in finite-dimensional setting, and also in an infinite-dimensional shift-invariant spaces.

六、附报告人简介:

孙颀彧教授,国际知名应用调和分析专家。主要研究领域包括应用与计算调和分析，采样理论和信号处理；已发表论文105篇（SCI），专著1本，2项研究报告，在重要国际会议上受邀作学术报告70余次；主持了4项美国国家自然科学基金。

担任以下SCI国际著名杂志的主编或编委：《Advances in Computational Mathematics》、《Numerical Functional Analysis and Optimization》、《Sampling Theory in Signal and Imaging Processing》和《Frontiers in Applied Mathematics and Statistics》。

欢迎广大师生参加！

理学院

应用数学研究所

2016年12月18日