arXiv subjects
Publications and source records attributed to C. Diogo.
We study the relations between maximal functions in a Toeplitz kernel and those in a subkernel of the same Toeplitz operator, as well as the question of how multipliers between Toeplitz kernels act on subkernels. We use those relations to obtain model space representations, in particular isometric model space representations and Hayashi's representation, for some important classes of Toeplitz kernels.
Toeplitz kernels can be defined by Riemann-Hilbert problems, by maximal functions, or by multipliers acting on model spaces. In this paper we study those different characterisations and their relations, highlighting, on the one hand, the crucial role played by symbol factorisation in obtaining multipliers from a model space onto a Toeplitz kernel, in particular isometric multipliers, and, on the other hand, a deep connection of maximal functions with a naturally defined conjugation on the Toeplitz kernel.
The solvability of the Riemann-Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener-Hopf type factorization with bounded outer factors but rather general diagonal elements of its middle factor. This covers, in particular, the almost periodic setting. Connections with the corona problem are discussed. Based on those, constructive factorization criteria are derived for several types of triangular 2-by-2 matrices.