中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
表示论研讨班
Speaker: 余君 教授 (北京国际数学研究中心)
Inviter: 聂思安
Language: Chinese
Title: Positivity of Fourier transform of zonal spherical functions
Time & Venue: 2026年5月21日（星期四）10: 00 - 11: 00 & N818
Abstract: Given a semisimple real or p-adic linear group, a zonal spherical function is matrix coefficient associated to the unique spherical vector with value 1 at identity element in a unitary spherical principal series. Each zonal spherical function is a positive definite function. Hence, its Fourier transform along a maximal split torus is everywhere non-negative by a classical theorem of Salomon Bochner. We showed the Fourier transform along a maximal split torus of any zonal spherical function takes positive value everywhere.
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