Mathematical Institute of the University of Bonn

RG Analysis and Partial Differential Equations

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

Winter Semester 2020/2021

Dr. Alex Amenta

Instructor

Prof. Dr. Christoph Thiele

Instructor

Lectures

• Tu 10-12
• Th 10-12

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.

Topics

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.

Prerequisites

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

Administration

Link to page in Basis

Literature

• T. Hytonen, J. van Neerven, M. Veraar, and L. Weis, Analysis in Banach Spaces (volumes I and II)
• G. Pisier, Martingales in Banach Spaces.