学术报告预告

题 目：Continuous framings for Banach spaces

报告人： 李鹏同教授（南京航空航天大学数学系）

摘 要：The theory of discrete and continuous frames was introduced for the purpose of analyzing and reconstructing signals mainly in Hilbert spaces. However, in many interesting applications the analyzed space is usually a Banach space, and consequently the stable analysis / reconstruction schemes need to be investigated for general Banach spaces. Parallel to discrete Hilbert space frames, the theory of atomic decompositions, p-frames and framings have been introduced in the literature to address this problem. In this paper we focus on continuous frames and continuous framings (alternatively, integral reconstructions) for Banach spaces by the means of g-Kothe function spaces. Necessary and sufficient conditions for a measurable function to be a continuous frame are obtained, and we obtain a decomposition result  for the analysis operators of continuous frames in terms of simple Kothe-Bochner operators. As a byproduct we show that a Riesz type continuous frame does not exist unless the associated measure space is purely atomic. One of our main results shows that there is an intrinsic connections between continuous framings and g-Kothe function spaces.

时 间： 2016年6月3日(星期五)9:00-10:00.

地 点： 数学科学学院三楼报告厅（304房间）

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李鹏同教授简介：李鹏同，男，博士、教授、博士生导师，2003至今任职于南京航空航天大学数学系。本科（1984）、硕士（1991）毕业于曲阜师范大学，博士毕业于浙江大学（2003），之后在南京大学做博士后研究（2001-2003）。主要研究方向为算子代数与框架理论. 主持2项国家自然科学基金（面上项目）和1项江苏省自然科学基金.在J. Funct. Anal., Numer. Funct. Anal. Optim., J. Operator Theory, Integr. Equ. Oper. Theory, Adv. Comput. Math.等刊物上发表SCI论文27 篇, 合作出版专著1部.