中科院数学与系统科学研究院

数学研究所

  中科院华罗庚数学重点实验室 

多复变与复几何学术年活动

Some Topics in Several Complex Variables

Speaker：Prof. Genkai Zhang (University of Gothenburg) 

Title：Weighed Bergman spaces on Siegel-Jacobi spaces:I. Reproducing kernels and analytic continuation, discrete spectrum of  Laplace operators;II. Bilinear-invariant differential operators.

Time：07.21,09:30—11:30

Venue：N902

Abstract：In Part I, I'll study weighted Bergman spaces on the Siegel-Jacobi spaces and  their analytic continuation, finding the corresponding Wallach set. We prove that the  Jacobi-group invariant Laplace operator has positive eigenvalues above the zero eigenvalue (whose eigenspace is the weighted Bergman space). In Part II, I'll find a decomposition of tensor-products of the weighted Bergman spaces and the corresponding Rankin-Cohen brackets, generalizing my earlier work with Lizhong Peng.