Title: Multipliers on Lie groups of exponential growth
Speaker: Zhipeng Song（Universite de Marie et Louis Pasteur & Ghent University）
Time: Wednesday, March 11, 2026, 16:00-17:30 (UTC+8)
Venue: Gewu Building, Room 315
Zoom ID: 954 5584 5933 (Password: 303985)
Link: https://zoom.us/j/95455845933?pwd=wmF4Bakfq6VzhZdkqmc0U49AHd2OcF.1
Abstract: Let G/K be a noncompact Riemannian symmetric space, where G is a noncompact connected semisimple Lie group with finite center, and view G/K also as a solvable non-unimodular group S = AN via the Iwasawa decomposition G = ANK of G. We focus on estimates for the kernels of spectral multipliers F(L) for two Laplace-like operators L: the shifted Laplace-Beltrami operator ∆ρ of G/K and the distinguished Laplacian L of S. Although related, these two operators are known to behave quite differently. First, for the general Borel function F, we impose a condition on F so that the kernel is uniformly bounded. Then, we pass to oscillatory functions of type 
= eit 
, which are critical for solving wave-type equations on symmetric spaces. We give a condition on the function ψ such that the kernel of Ψ(L) is L1 bounded. This is a joint work with Yulia Kuznetsova.
