Mathematical Sciences: Research in Harmonic Analysis

DMS-9501191 PI：大体 格罗斯将继续他的研究算子值贝塞尔函数域的积极性，超几何函数的高维空间，多维扩展拉马努金的主定理，并将推广到设置对称锥，结构从经典分析和近似理论有关牛顿多项式。 此外，格罗斯将开发一个理论的特殊功能，将适用于非对称锥中出现的理论李群，调查交织运营商相关的退化主要系列表示约化李群，并研究特殊功能相关的光锥和不确定的正交群的秩二。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。

DMS-9501191 PI: Gross Gross will continue his research on operator-valued Bessel functions on domains of positivity, hypergeometric functions on higher-dimensional spaces, multidimensional extensions of Ramanujan's Master Theorem, and will generalize to the setting of symmetric cones, constructs from classical analysis and approximation theory related to Newton polynomials. Also, Gross will develop a theory of special functions that will apply to non-symmetric cones that arise in the theory of Lie groups, investigate intertwining operators associated to degenerate principal series representations of reductive Lie groups, and study special functions associated to light cones and the indefinite orthogonal groups of rank two. 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.