Spectral Approximation of Transfer Operators

Explore a 46-minute lecture on spectral approximation of transfer operators, delivered by Oscar Bandtlow as part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference. Delve into the challenge of approximating spectral data of transfer operators, particularly those relevant to number theory applications. Learn about an easily implementable Galerkin-type method using Lagrange–Chebyshev interpolation and its convergence properties. Examine topics such as projection methods, Ulam methods, a priori error estimates, and convergence results for analytic and smooth cases. Discover the application of these concepts to resonances of Schottky surfaces and gain insights into the historical context of transfer operators in mathematics.

Intro
Setup
Calculating spectral data of transfer operators Potted history
Projection method
Ulam method
A priori error estimates
Lagrange-Chebyshev interpolation
Convergence results: analytic case
Convergence results: smooth case
Convergence results for Fredholm determinants
Application: resonances of Schottky surfaces