Mathematical Sciences: Harmonic Analysis and Group Representation

PI：丁丁将研究对称锥和对称西格尔域上算子值贝塞尔函数的解析延拓；特别是算子值贝塞尔函数在这些域的边界分量上。利用贝塞尔函数的解析延拓，他将研究这些域的自同构群的调和表示的分解。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

DMS-9500905 PI: Ding Ding will study analytic continuation of operator-valued Bessel functions on symmetric cones and symmetric Siegel domains; in particular, operator valued Bessel functions on boundary components of these domains. Using analytic continuation of Bessel functions, he will study the decomposition of the harmonic representation of automorphism groups of these domains. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.