Toeplitz kernels and model spaces

Abstract

We review some classical and more recent results concerning kernels of Toeplitz operators and their relations with model spaces, which are themselves Toeplitz kernels of a special kind. We highlight the fundamental role played by the existence of maximal vectors for every nontrivial Toeplitz kernel.

20 pages, based on talk given at IWOTA 2017. This version incorporates some minor corrections