Self-adjoint truncated Toeplitz operators on finite-dimensional model spaces

A truncated Toeplitz operator is the compression of a Toeplitz operator on the Hardy space H2H2 to a model subspace of H2H2. Such an operator has a family of symbols, and a basic goal is to understand the interplay between the operator, qua operator, and its symbols. This paper studies the question for self-adjoint truncated Toeplitz operators on finite-dimensional model spaces. The main focus is the two-dimensional case.