RG Analysis and Partial Differential Equations

V5B7: Selected Topics in Analysis - Introduction to Banach-valued analysis

Winter Semester 2020/2021

Dr. Alex Amenta
Prof. Dr. Christoph Thiele


Lectures will take place online, with recordings made available afterwards. Typed lecture notes will be available in advance. Please contact the instructors for Zoom information.


Many results of the analysis of scalar-valued functions extend to functions valued in infinite-dimensional Banach spaces. Carrying out these extensions relies on (and reveals) subtle connections between Fourier analysis, probability, operator theory, and the geometry of Banach spaces. This course will cover some of the fundamental topics in the analysis of Banach-valued functions, including Bochner spaces, martingales, UMD Banach spaces, Fourier multipliers (including the Hilbert transform), and Rademacher type and cotype. Further topics will be announced as the course progresses. More information will be made available here.


Functional analysis (particularly Banach spaces) and measure theory. Experience with Fourier analysis and probability is recommended but not required.


Link to page in Basis