Harold Widom’s Contributions to the Spectral Theory and Asymptotics of Toeplitz Operators and Matrices

This is a survey of Harold Widom’s work in the spectral theory of Toeplitz and Wiener-Hopf operators and on asymptotic problems for truncations of these operators as the truncation parameter goes to infinity. The asymptotic problems include Toeplitz and Wiener-Hopf determinants, extreme eigenvalues, and collective eigenvalue distribution. Harold Widom has made groundbreaking contributions to all these topics.