Introduction to Frames and Riesz Bases - Part 2

Explore the second part of a mini-course on frames and Riesz bases presented by Ole Christensen from the Technical University of Denmark. Delve into advanced topics in analytic function spaces, including the Fourier transform, classical wavelet theory, and spline wavelet frames. Examine the shortcomings of the Unitary Extension Principle (UEP) and discover more recent extension principles. Investigate Gabor frames and Riesz bases, their relationship with B-splines, and the duals of Gabor frames. Conclude with an explicit construction of dual pairs of Gabor frames. This 53-minute lecture, part of the Focus Program on Analytic Function Spaces and their Applications, offers a comprehensive exploration of these fundamental concepts in mathematical analysis.

Intro
The Fourier transform
Classical wavelet theory
Spline wavelet frames
Shortcomings of the UEP
More recent extension principles
Gabor frames and Riesz bases
Gabor frames and B-splines
The duals of a Gabor frame
Explicit construction of dual pairs of Gabor frames