【讲座题目】 Stable phase retrieval and Banach lattices
【主 讲 人】 Timur Oikhberg教授
【讲座时间】 2024年06月24日 星期一 上午10:00-11:00
【讲座地点】主楼 C636
【主讲人简介】 Timur Oikhberg， 美国伊利诺伊大学厄巴纳-香槟分校教授。主要研究方向为泛函分析，包括Banach空间理论，Banach格和逼近理论。在Journal of Functional Analysis, Mathematische Annalen, Journal of the European Mathematical Society, Mathematische Zeitschrift, Journal of Mathematical Analysis and Applications, Proceedings of the American Mathematical Society等期刊发表学术论文70余篇。
【讲座内容简介】 The problem of phase retrieval originates in the need to reconstruct a signal from its absolute value. Here we focus on "robust" reconstruction - that is, small changes in the absolute value produce small changes in the signal to be reconstructed; this is stable phase retrieval. We consider the problem in for subspaces of Banach lattices. In this setting, a connection between the possibility of stable phase retrieval and the existence of "almost disjoint" elements can be found. For certain classes of lattices - such as $L_p$ spaces - we obtain a convenient description of subspaces which permit stable phase retrieval. For $C(K)$ spaces, the situation is less clear, but still, some partial results can be obtained.
