Function Spaces on Quantum Tori and Their Applications
Offered By: BIMSA via YouTube
Course Description
Overview
Explore function spaces on quantum tori and their applications in this 53-minute conference talk by Xiao Xiong at BIMSA. Delve into the definitions of Sobolev, Besov, and Triebel-Lizorkin spaces on quantum tori, and discover how functional analysis methods are adapted to these spaces. Examine fundamental properties, including the lifting theorem, embedding inequalities, and Littlewood-Paley type characterizations for Besov and Triebel-Lizorkin spaces. Learn about concrete characterizations using Poisson and heat semigroups, as well as differences. Conclude with two practical applications of function space theory: pseudo-differential theory and Connes' noncommutative geometry.
Syllabus
Xiao Xiong: Function spaces on quantum tori and their applications #ICBS2024
Taught by
BIMSA
Related Courses
An Introduction to Functional AnalysisÉcole Centrale Paris via Coursera Sobolev Spaces and Partial Differential Equations
IMSC via Swayam The Computational Theory of Riemann-Hilbert Problems - Lecture 4
International Centre for Theoretical Sciences via YouTube Sobolev Regularity for Maximal Operators
Hausdorff Center for Mathematics via YouTube The Regularity Problem for the Laplace Equation in Rough Domains
Hausdorff Center for Mathematics via YouTube