Mathematical Sciences: Harmonic Analysis and Group Representation

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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.