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120周年校庆系列学术活动: Spherical Operators

主 讲 人 :Gadadhar Misra    教授

活动时间:05月21日16时30分    

地      点 :Tencent会议:#VooV Meeting: 931-073-004

讲座内容:

Let B_d be the open Euclidean ball in C_d and T := (T1….. Td) be a commuting tuple of bounded linear operators on a complex separable Hilbert space H. Let U(d) be the linear group of unitary transformations acting on C_d by the rule: z:\rightarrow u.z, z\in C_d, where u _ z is the usual matrix product. Let u1(z),…., ud(z) be the coordinate functions of uz. We define uT to be the operator (u1(T ),….,ud(T )) and say that T is U(d)-homogeneous if u T is unitarily equivalent to T for all u\in U(d). In this talk, we describe U(d)-homogeneous tuples M of multiplication by coordinate functions acting on some reproducing kernel Hilbert space HK(Bd;Cn) \subset Hol(Bd;Cn), where n is the dimension of the joint kernel of the d-tuple T. The case of n = 1 is well understood, here, we focus on the case of n = d. We describe a large class of U(d)-homogeneous operators and obtain explicit criterion for (i) boundedness, (ii) reducibility and (iii) mutual unitary equivalence of these operators. Finally, we classify the kernels K taking values in Mn(C), 1 \leq n \leq d, quasi-invariant under an irreducible unitary representation c of the group U(d). A crucial ingredient of this proof is that the group SU(d) has exactly two inequivalent irreducible unitary representations of dimension d and none in dimensions 2,…, d - 1, d> 2.


主讲人先容:

Gadadhar Misra, 现任印度理工学院甘地分校(The Indian Institute of Technology Gandhinagar )教授,印度科学院院士(Fellow, Indian Academy of Sciences)、印度国家科学院副主席(Vice-President,Indian National Science Academy)、国家科学学院院士(National Academy of Sciences, India)、J C Bose National Fellowship,曾荣获Shanti Swarup Bhatnagar (SSB) Prize(印度科学与工业最高奖)、Biju Patnaik Award for Scientific Excellence(奥迪沙政府科技部科学卓越奖)等奖励,主要研究方向为Cowen-Douglas算子理论、解析模理论以及群表示理论,代表性成果发表在Adv. Math、J. Reine Angew. Math.、Proc. London Math.Soc.、J. Funct. Anal.、Trans. Amer. Math. Soc、Israel J Math.等国际权威数学杂志上。


发布时间:2022-05-20 21:44:00

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地址:河北省石家庄市南二环东路20号 邮编:050024 

版权所有雷竞技官网

冀ICP备18011017号-3

冀公网安备 13010802000630号

地址:河北省石家庄市南二环东路20号

邮编:050024 

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