Spectral properties of Krein-Feller operators
Organizers
Speaker
Time
Tuesday, November 5, 2024 3:00 PM - 4:00 PM
Venue
A7-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
A Krein-Feller operator is a Laplacian defined on a domain by a measure. The spectral dimension of a Krein-Feller operator is a fundamental quantity that plays an important role in studying the analytic properties of the operator. We report some results concerning the spectral dimension of Krein-Feller operators defined by fractal measures, focusing on self-similar measures with overlaps. We discuss some applications, including heat kernel estimates and wave propagation speed. We also discuss the extension of such Laplacians to Riemannian manifolds. This talk is based on joint work with Qingsong Gu, Jiaxin Hu, Lei Ouyang, Wei Tang, and Yuanyuan Xie.
Speaker Intro
Dr. Ngai received his B.Sc. from University of Hong Kong, and his M.A. and Ph.D. from University of Pittsburgh. After receiving his Ph.D., he has held research and teaching positions at The Chinese University of Hong Kong, Cornell University, Georgia Institute of Technology, and Georgia Southern University. He joined Beijing Institute of Mathematical Sciences and Applications as a professor in 2024. His main research areas are fractal geometry and the theory of fractal measures. He is also interested in the theories of wavelets, self-affine tiles, fractal differential equations, and spectral graph theory.