Introduction to Frames and Riesz Bases - Part 3

Delve into the third part of a mini-course on frames and Riesz bases, presented by Ole Christensen from the Technical University of Denmark. Begin with a recap of key concepts from the second lecture before exploring general wavelet frames. Examine the extension of Bessel sequences to tight frames, with a focus on Gabor Bessel sequences. Investigate the extension of Bessel sequences to dual frames and dual frame pairs, particularly in the context of Gabor and wavelet systems. Learn about Dynamical Sampling from 2015 and review relevant literature results. Analyze the existence of representations and operator representations of Gabor frames. Conclude with a prologue discussing a frame where no subsequence forms a basis. This 55-minute lecture, part of the Focus Program on Analytic Function Spaces and their Applications, offers an in-depth look at advanced topics in frame theory.

Intro
Key parts from the second lecture
General wavelet frames
Extension of Bessel sequences to tight frames
Extension of Gabor Bessel sequences to tight frames
Extension of Bessel sequences to dual frames
Extension of Gabor Bessel sequences to dual frame pairs
The wavelet case
Dynamical Sampling, 2015
Results from the literature
Existence of the representation
Operator representations of Gabor frames
Prologue: A frame where no subsequence is a basis